diff --git a/.appveyor.yml b/.appveyor.yml
index f8cd85f17dcb..20807e36e6f5 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -7,6 +7,8 @@ configuration:  # a trick to construct a build matrix with multiple Python versi
 
 environment:
   matrix:
+    - COMPILER: MINGW
+      TASK: r-package
     - COMPILER: MSVC
       TASK: python
     - COMPILER: MINGW
diff --git a/.ci/test_r_package_windows.ps1 b/.ci/test_r_package_windows.ps1
new file mode 100644
index 000000000000..5bd65d28408b
--- /dev/null
+++ b/.ci/test_r_package_windows.ps1
@@ -0,0 +1,108 @@
+# Download a file and retry upon failure. This looks like
+# an infinite loop but CI-level timeouts will kill it
+function Download-File-With-Retries {
+  param(
+    [string]$url,
+    [string]$destfile
+  )
+  do {
+    Write-Output "Downloading ${url}"
+    sleep 5;
+    (New-Object System.Net.WebClient).DownloadFile($url, $destfile)
+  } while(!$?);
+}
+
+$env:R_WINDOWS_VERSION = "3.6.3"
+$env:R_LIB_PATH = "$env:BUILD_SOURCESDIRECTORY/RLibrary" -replace '[\\]', '/'
+$env:PATH = "$env:R_LIB_PATH/Rtools/bin;" + "$env:R_LIB_PATH/R/bin/x64;" + "$env:R_LIB_PATH/miktex/texmfs/install/miktex/bin/x64;" + $env:PATH
+$env:CRAN_MIRROR = "https://cloud.r-project.org/"
+$env:CTAN_MIRROR = "https://ctan.math.illinois.edu/systems/win32/miktex/tm/packages/"
+
+if ($env:COMPILER -eq "MINGW") {
+  $env:CXX = "$env:R_LIB_PATH/Rtools/mingw_64/bin/g++.exe"
+  $env:CC = "$env:R_LIB_PATH/Rtools/mingw_64/bin/gcc.exe"
+}
+
+cd $env:BUILD_SOURCESDIRECTORY
+tzutil /s "GMT Standard Time"
+[Void][System.IO.Directory]::CreateDirectory($env:R_LIB_PATH)
+
+if ($env:COMPILER -eq "MINGW") {
+  Write-Output "Telling R to use MinGW"
+  $install_libs = "$env:BUILD_SOURCESDIRECTORY/R-package/src/install.libs.R"
+  ((Get-Content -path $install_libs -Raw) -replace 'use_mingw <- FALSE','use_mingw <- TRUE') | Set-Content -Path $install_libs
+}
+
+# download R and RTools
+Write-Output "Downloading R and Rtools"
+Download-File-With-Retries -url "https://cloud.r-project.org/bin/windows/base/old/$env:R_WINDOWS_VERSION/R-$env:R_WINDOWS_VERSION-win.exe" -destfile "R-win.exe"
+Download-File-With-Retries -url "https://cloud.r-project.org/bin/windows/Rtools/Rtools35.exe" -destfile "Rtools.exe"
+
+# Install R
+Write-Output "Installing R"
+Start-Process -FilePath R-win.exe -NoNewWindow -Wait -ArgumentList "/VERYSILENT /DIR=$env:R_LIB_PATH/R /COMPONENTS=main,x64" ; Check-Output $?
+Write-Output "Done installing R"
+
+Write-Output "Installing Rtools"
+Start-Process -FilePath Rtools.exe -NoNewWindow -Wait -ArgumentList "/VERYSILENT /DIR=$env:R_LIB_PATH/Rtools" ; Check-Output $?
+Write-Output "Done installing Rtools"
+
+# MiKTeX and pandoc can be skipped on non-MINGW builds, since we don't
+# build the package documentation for those
+if ($env:COMPILER -eq "MINGW") {
+    Write-Output "Downloading MiKTeX"
+    Download-File-With-Retries -url "https://miktex.org/download/win/miktexsetup-x64.zip" -destfile "miktexsetup-x64.zip"
+    Add-Type -AssemblyName System.IO.Compression.FileSystem
+    [System.IO.Compression.ZipFile]::ExtractToDirectory("miktexsetup-x64.zip", "miktex")
+    Write-Output "Setting up MiKTeX"
+    .\miktex\miktexsetup.exe --remote-package-repository="$env:CTAN_MIRROR" --local-package-repository=./miktex/download --package-set=essential --quiet download ; Check-Output $?
+    Write-Output "Installing MiKTeX"
+    .\miktex\download\miktexsetup.exe --remote-package-repository="$env:CTAN_MIRROR" --portable="$env:R_LIB_PATH/miktex" --quiet install ; Check-Output $?
+    Write-Output "Done installing MiKTeX"
+
+    initexmf --set-config-value [MPM]AutoInstall=1
+    conda install -q -y --no-deps pandoc
+}
+
+Add-Content .Renviron "R_LIBS=$env:R_LIB_PATH"
+
+Write-Output "Installing dependencies"
+$packages = "c('data.table', 'jsonlite', 'Matrix', 'R6', 'testthat'), dependencies = c('Imports', 'Depends', 'LinkingTo')"
+Rscript --vanilla -e "options(install.packages.check.source = 'no'); install.packages($packages, repos = '$env:CRAN_MIRROR', type = 'binary', lib = '$env:R_LIB_PATH')" ; Check-Output $?
+
+Write-Output "Building R package"
+Rscript build_r.R --skip-install ; Check-Output $?
+
+$PKG_FILE_NAME = Get-Item *.tar.gz
+$LOG_FILE_NAME = "lightgbm.Rcheck/00check.log"
+
+$env:_R_CHECK_FORCE_SUGGESTS_ = 0
+if ($env:COMPILER -ne "MINGW") {
+  Write-Output "Running R CMD check without checking documentation"
+  R.exe CMD check --no-multiarch --no-examples --no-manual --ignore-vignettes ${PKG_FILE_NAME} ; $check_succeeded = $?
+} else {
+  Write-Output "Running R CMD check as CRAN"
+  R.exe CMD check --no-multiarch --as-cran ${PKG_FILE_NAME} ; $check_succeeded = $?
+}
+
+Write-Output "R CMD check build logs:"
+Get-Content -Path $env:BUILD_SOURCESDIRECTORY\lightgbm.Rcheck\00install.out
+
+Check-Output $check_succeeded
+
+Write-Output "Looking for issues with R CMD check results"
+if (Get-Content "$LOG_FILE_NAME" | Select-String -Pattern "WARNING" -Quiet) {
+    echo "WARNINGS have been found by R CMD check!"
+    Check-Output $False
+}
+
+$note_str = Get-Content "${LOG_FILE_NAME}" | Select-String -Pattern ' NOTE' | Out-String ; Check-Output $?
+$relevant_line = $note_str -match '.*Status: (\d+) NOTE.*'
+$NUM_CHECK_NOTES = $matches[1]
+$ALLOWED_CHECK_NOTES = 3
+if ([int]$NUM_CHECK_NOTES -gt $ALLOWED_CHECK_NOTES) {
+    Write-Output "Found ${NUM_CHECK_NOTES} NOTEs from R CMD check. Only ${ALLOWED_CHECK_NOTES} are allowed"
+    Check-Output $False
+}
+
+Write-Output "No issues were found checking the R package"
diff --git a/.ci/test_windows.ps1 b/.ci/test_windows.ps1
index 82849577152d..fd0e9f95a5e4 100644
--- a/.ci/test_windows.ps1
+++ b/.ci/test_windows.ps1
@@ -12,6 +12,11 @@ if (Test-Path env:APPVEYOR) {
   $env:BUILD_SOURCESDIRECTORY = $env:APPVEYOR_BUILD_FOLDER
 }
 
+if ($env:TASK -eq "r-package") {
+  & $env:BUILD_SOURCESDIRECTORY\.ci\test_r_package_windows.ps1 ; Check-Output $?
+  Exit 0
+}
+
 # setup for Python
 conda init powershell
 conda activate
diff --git a/.vsts-ci.yml b/.vsts-ci.yml
index a39dbc0e105b..a533ab1659e4 100644
--- a/.vsts-ci.yml
+++ b/.vsts-ci.yml
@@ -22,7 +22,7 @@ jobs:
     vmImage: 'ubuntu-latest'
   container: ubuntu1404
   strategy:
-    maxParallel: 6
+    maxParallel: 7
     matrix:
       regular:
         TASK: regular
@@ -76,7 +76,7 @@ jobs:
   pool:
     vmImage: 'macOS-10.14'
   strategy:
-    maxParallel: 3
+    maxParallel: 4
     matrix:
       regular:
         TASK: regular
@@ -117,8 +117,11 @@ jobs:
   pool:
     vmImage: 'vs2017-win2016'
   strategy:
-    maxParallel: 3
+    maxParallel: 4
     matrix:
+      r_package:
+        TASK: r-package
+        COMPILER: MINGW
       regular:
         TASK: regular
         PYTHON_VERSION: 3.6
diff --git a/R-package/NAMESPACE b/R-package/NAMESPACE
index 7aef39a1f6de..14db7ba98d6c 100644
--- a/R-package/NAMESPACE
+++ b/R-package/NAMESPACE
@@ -36,6 +36,7 @@ export(saveRDS.lgb.Booster)
 export(setinfo)
 export(slice)
 import(methods)
+importFrom(Matrix,Matrix)
 importFrom(R6,R6Class)
 importFrom(data.table,":=")
 importFrom(data.table,as.data.table)
diff --git a/R-package/R/lightgbm.R b/R-package/R/lightgbm.R
index 9459ccc4d5c4..12640ecfb0af 100644
--- a/R-package/R/lightgbm.R
+++ b/R-package/R/lightgbm.R
@@ -178,6 +178,7 @@ NULL
 
 # Various imports
 #' @import methods
+#' @importFrom Matrix Matrix
 #' @importFrom R6 R6Class
 #' @useDynLib lib_lightgbm , .registration = TRUE
 NULL
diff --git a/R-package/src/cmake/modules/FindLibR.cmake b/R-package/src/cmake/modules/FindLibR.cmake
index 20c0a974e1ff..ad26f06dfeef 100644
--- a/R-package/src/cmake/modules/FindLibR.cmake
+++ b/R-package/src/cmake/modules/FindLibR.cmake
@@ -174,17 +174,31 @@ execute_process(
   OUTPUT_VARIABLE LIBR_LIB_DIR
 )
 
+set(LIBR_HOME ${LIBR_HOME} CACHE PATH "R home directory")
+set(LIBR_EXECUTABLE ${LIBR_EXECUTABLE} CACHE PATH "R executable")
+set(LIBR_INCLUDE_DIRS ${LIBR_INCLUDE_DIRS} CACHE PATH "R include directory")
+set(LIBR_LIB_DIR ${LIBR_LIB_DIR} CACHE PATH "R shared libraries directory")
+
+# where is R.so / R.dll / libR.so likely to be found?
+set(LIBR_PATH_HINTS "${CMAKE_CURRENT_BINARY_DIR}" "${LIBR_LIB_DIR}" "${LIBR_HOME}/bin/${R_ARCH}" "${LIBR_HOME}/bin" "${LIBR_LIBRARIES}")
+
 # look for the core R library
 find_library(
   LIBR_CORE_LIBRARY
-  NAMES R
-  HINTS "${CMAKE_CURRENT_BINARY_DIR}" "${LIBR_LIB_DIR}" "${LIBR_HOME}/bin" "${LIBR_LIBRARIES}"
+  NAMES R R.dll
+  HINTS ${LIBR_PATH_HINTS}
 )
 
-set(LIBR_HOME ${LIBR_HOME} CACHE PATH "R home directory")
-set(LIBR_EXECUTABLE ${LIBR_EXECUTABLE} CACHE PATH "R executable")
-set(LIBR_INCLUDE_DIRS ${LIBR_INCLUDE_DIRS} CACHE PATH "R include directory")
-set(LIBR_LIB_DIR ${LIBR_LIB_DIR} CACHE PATH "R shared libraries directory")
+# starting from CMake 3.17, find_library() will not find .dll files by default
+# https://cmake.org/cmake/help/v3.17/release/3.17.html#other-changes
+if (WIN32 AND NOT LIBR_CORE_LIBRARY)
+    find_file(
+        LIBR_CORE_LIBRARY
+        NAME R.dll
+        HINTS ${LIBR_PATH_HINTS}
+    )
+endif()
+
 set(LIBR_CORE_LIBRARY ${LIBR_CORE_LIBRARY} CACHE PATH "R core shared library")
 
 if(WIN32 AND MSVC)
diff --git a/R-package/src/install.libs.R b/R-package/src/install.libs.R
index a79c93d846b7..339e8417ee70 100644
--- a/R-package/src/install.libs.R
+++ b/R-package/src/install.libs.R
@@ -67,6 +67,7 @@ if (!use_precompile) {
   # Check if Windows installation (for gcc vs Visual Studio)
   if (WINDOWS) {
     if (use_mingw) {
+      print("Trying to build with MinGW")
       cmake_cmd <- paste0(cmake_cmd, " -G \"MinGW Makefiles\" ")
       build_cmd <- "mingw32-make.exe _lightgbm"
       system(paste0(cmake_cmd, " ..")) # Must build twice for Windows due sh.exe in Rtools