diff --git a/src/treelearner/serial_tree_learner.cpp b/src/treelearner/serial_tree_learner.cpp
index 304c712f0723..9ea50e148901 100644
--- a/src/treelearner/serial_tree_learner.cpp
+++ b/src/treelearner/serial_tree_learner.cpp
@@ -683,7 +683,8 @@ void SerialTreeLearner::SplitInner(Tree* tree, int best_leaf, int* left_leaf,
 
   // init the leaves that used on next iteration
   if (best_split_info.left_count < best_split_info.right_count) {
-    CHECK_GT(best_split_info.left_count, 0);
+    if (best_split_info.left_count == 0)
+      Log::Warning("Best split left count is 0 for leaf %d", *left_leaf);
     smaller_leaf_splits_->Init(*left_leaf, data_partition_.get(),
                                best_split_info.left_sum_gradient,
                                best_split_info.left_sum_hessian,
@@ -693,7 +694,8 @@ void SerialTreeLearner::SplitInner(Tree* tree, int best_leaf, int* left_leaf,
                               best_split_info.right_sum_hessian,
                               best_split_info.right_output);
   } else {
-    CHECK_GT(best_split_info.right_count, 0);
+    if (best_split_info.right_count == 0)
+      Log::Warning("Best split right count is 0 for leaf %d", *right_leaf);
     smaller_leaf_splits_->Init(*right_leaf, data_partition_.get(),
                                best_split_info.right_sum_gradient,
                                best_split_info.right_sum_hessian,
@@ -735,7 +737,8 @@ void SerialTreeLearner::RenewTreeOutput(Tree* tree, const ObjectiveFunction* obj
         const double new_output = obj->RenewTreeOutput(output, residual_getter, index_mapper, bag_mapper, cnt_leaf_data);
         tree->SetLeafOutput(i, new_output);
       } else {
-        CHECK_GT(num_machines, 1);
+        if (num_machines <= 1)
+          Log::Warning("num_machines less or equal to 1 for leaf %d, num_machines is %d", i, num_machines);
         tree->SetLeafOutput(i, 0.0);
         n_nozeroworker_perleaf[i] = 0;
       }
diff --git a/tests/python_package_test/test_engine.py b/tests/python_package_test/test_engine.py
index d44e5848fe7c..0cdaa8988868 100644
--- a/tests/python_package_test/test_engine.py
+++ b/tests/python_package_test/test_engine.py
@@ -9,6 +9,7 @@
 from pathlib import Path
 
 import numpy as np
+import pandas as pd
 import psutil
 import pytest
 from scipy.sparse import csr_matrix, isspmatrix_csc, isspmatrix_csr
@@ -3458,3 +3459,54 @@ def test_boost_from_average_with_single_leaf_trees():
     preds = model.predict(X)
     mean_preds = np.mean(preds)
     assert y.min() <= mean_preds <= y.max()
+
+
+@pytest.mark.parametrize('device', ['cpu'])
+def test_training_leaf_count_zero(device):
+    # test data is prepared produce one of the following errors (without the fix):
+    #    Check failed: (best_split_info.left_count) > (0)
+    #    Check failed: (best_split_info.right_count) > (0)
+    # The issues related to this tests are:
+    # https://github.com/microsoft/LightGBM/issues/4946
+
+    # Make random data with the seed
+    R, C = 100000, 10
+    if device == 'cpu':
+        np.random.seed(0)
+    else:
+        np.random.seed(50)
+    data = pd.DataFrame(np.random.randn(R, C), dtype=np.float32)
+    for i in range(1, C):
+        data[i] += data[0] * np.random.randn()
+
+    # Split train/test = 60/40
+    N = int(0.6 * len(data))
+    train_data = data.loc[:N]
+    test_data = data.loc[N:]
+
+    train = lgb.Dataset(train_data.iloc[:, 1:], train_data.iloc[:, 0], free_raw_data=True)
+    test = lgb.Dataset(test_data.iloc[:, 1:], test_data.iloc[:, 0], free_raw_data=True, reference=train)
+
+    # The test is run twice, on cpu and gpu
+    params = {
+        'device': device,
+        'boosting_type': 'gbdt',
+        'objective': 'regression',
+        'max_tree_output': 0.03,
+        'max_bin': 20,
+        'max_depth': 10,
+        'num_leaves': 127,
+        'seed': 8,
+        'learning_rate': 0.01,
+        'bagging_fraction': 0.5,
+        'bagging_freq': 1,
+        'min_data_in_leaf': 0,
+        'verbose': -1,
+        'min_split_gain': 0.1,
+        'cegb_penalty_feature_coupled': 5 * np.ones(C - 1),
+        'cegb_penalty_split': 0.0000002,
+    }
+
+    # The code without the fix will break on the following line
+    gbm = lgb.train(params, train, num_boost_round=5000, valid_sets=test)
+    assert True