diff --git a/.ci/test.sh b/.ci/test.sh
index 435614bb826f..6e553637b86b 100755
--- a/.ci/test.sh
+++ b/.ci/test.sh
@@ -16,7 +16,7 @@ cd $BUILD_DIRECTORY
 if [[ $TRAVIS == "true" ]] && [[ $TASK == "check-docs" ]]; then
     cd $BUILD_DIRECTORY/docs
     conda install -q -y -n $CONDA_ENV -c conda-forge doxygen
-    pip install --user -r requirements.txt rstcheck
+    pip install --user -r requirements.txt rstcheck git+git://github.com/linkchecker/linkchecker.git@b9390c9ef63f7e1e210b48bc7fe97f76e8d39501
     # check reStructuredText formatting
     cd $BUILD_DIRECTORY/python-package
     rstcheck --report warning `find . -type f -name "*.rst"` || exit -1
@@ -26,11 +26,7 @@ if [[ $TRAVIS == "true" ]] && [[ $TASK == "check-docs" ]]; then
     make html || exit -1
     find ./_build/html/ -type f -name '*.html' -exec \
     sed -i'.bak' -e 's;\(\.\/[^.]*\.\)rst\([^[:space:]]*\);\1html\2;g' {} \;  # emulate js function
-    if [[ $OS_NAME == "linux" ]]; then
-        sudo apt-get update
-        sudo apt-get install linkchecker
-        linkchecker --config=.linkcheckerrc ./_build/html/*.html || exit -1
-    fi
+    linkchecker --config=.linkcheckerrc ./_build/html/*.html || exit -1
     # check the consistency of parameters' descriptions and other stuff
     cp $BUILD_DIRECTORY/docs/Parameters.rst $BUILD_DIRECTORY/docs/Parameters-backup.rst
     cp $BUILD_DIRECTORY/src/io/config_auto.cpp $BUILD_DIRECTORY/src/io/config_auto-backup.cpp
diff --git a/.travis.yml b/.travis.yml
index bc7b0d893529..2931492679bc 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,7 +9,7 @@ git:
 os:
   - linux
   - osx
-dist: bionic
+dist: focal
 osx_image: xcode12
 
 env:
diff --git a/docs/.linkcheckerrc b/docs/.linkcheckerrc
index 4a1cd072af0b..346a1505f877 100644
--- a/docs/.linkcheckerrc
+++ b/docs/.linkcheckerrc
@@ -6,7 +6,6 @@ sslverify=0
 [filtering]
 ignore=
   pythonapi/lightgbm\..*\.html.*
-  http://sphinx-doc.org
 ignorewarnings=http-robots-denied,https-certificate-error
 checkextern=1