diff --git a/python/src/spark_rapids_ml/classification.py b/python/src/spark_rapids_ml/classification.py
index 878d6256..a1c1af57 100644
--- a/python/src/spark_rapids_ml/classification.py
+++ b/python/src/spark_rapids_ml/classification.py
@@ -976,6 +976,12 @@ def _single_fit(init_parameters: Dict[str, Any]) -> Dict[str, Any]:
                     "dtype": logistic_regression.dtype.name,
                     "num_iters": logistic_regression.solver_model.num_iters,
                 }
+
+                if len(logistic_regression.classes_) == 1:
+                    if init_parameters["fit_intercept"] is True:
+                        model["coef_"] = [[0.0] * logistic_regression.n_cols]
+                        model["intercept_"] = [float("inf")]
+
                 del logistic_regression
                 return model
 
@@ -1027,6 +1033,16 @@ def _out_schema(self) -> Union[StructType, str]:
         )
 
     def _create_pyspark_model(self, result: Row) -> "LogisticRegressionModel":
+        if len(result["classes_"]) == 1:
+            if self.getFitIntercept() is False:
+                print(
+                    "WARNING: All labels belong to a single class and fitIntercept=false. It's a dangerous ground, so the algorithm may not converge."
+                )
+            else:
+                print(
+                    "WARNING: All labels are the same value and fitIntercept=true, so the coefficients will be zeros. Training is not needed."
+                )
+
         return LogisticRegressionModel._from_row(result)
 
     def _set_cuml_reg_params(self) -> "LogisticRegression":
diff --git a/python/tests/test_logistic_regression.py b/python/tests/test_logistic_regression.py
index f2f92d0f..62855b03 100644
--- a/python/tests/test_logistic_regression.py
+++ b/python/tests/test_logistic_regression.py
@@ -1076,3 +1076,71 @@ def test_parameters_validation() -> None:
         # charge of validating it.
         with pytest.raises(ValueError, match="C or regParam given invalid value -1.0"):
             LogisticRegression().setRegParam(-1.0).fit(df)
+
+
+@pytest.mark.compat
+@pytest.mark.parametrize("fit_intercept", [True, False])
+@pytest.mark.parametrize(
+    "lr_types",
+    [
+        # (SparkLogisticRegression, SparkLogisticRegressionModel),
+        (LogisticRegression, LogisticRegressionModel),
+    ],
+)
+def test_compat_one_label(
+    fit_intercept: bool,
+    lr_types: Tuple[LogisticRegressionType, LogisticRegressionModelType],
+    tmp_path: str,
+) -> None:
+    tolerance = 0.001
+    _LogisticRegression, _LogisticRegressionModel = lr_types
+
+    X = np.array(
+        [
+            [1.0, 2.0],
+            [1.0, 3.0],
+            [2.0, 1.0],
+            [3.0, 1.0],
+        ]
+    )
+    y = np.array(
+        [
+            1.0,
+            1.0,
+            1.0,
+            1.0,
+        ]
+    )
+    num_rows = len(X)
+
+    weight = np.ones([num_rows])
+    feature_cols = ["c0", "c1"]
+    schema = ["c0 float, c1 float, weight float, label float"]
+
+    with CleanSparkSession() as spark:
+        np_array = np.concatenate(
+            (X, weight.reshape(num_rows, 1), y.reshape(num_rows, 1)), axis=1
+        )
+
+        bdf = spark.createDataFrame(
+            np_array.tolist(),
+            ",".join(schema),
+        )
+
+        bdf = bdf.withColumn("features", array_to_vector(array(*feature_cols))).drop(
+            *feature_cols
+        )
+
+        blor = _LogisticRegression(
+            regParam=0.1, fitIntercept=fit_intercept, standardization=False
+        )
+        blor_model = blor.fit(bdf)
+
+        if fit_intercept is False:
+            assert array_equal(
+                blor_model.coefficients.toArray(), [0.85431526, 0.85431526], tolerance
+            )
+            assert blor_model.intercept == 0.0
+        else:
+            assert array_equal(blor_model.coefficients.toArray(), [0, 0], 0.0)
+            assert blor_model.intercept == float("inf")