diff --git a/tests/python_package_test/test_dask.py b/tests/python_package_test/test_dask.py
index dccc4065ba5..ff1fb2e155e 100644
--- a/tests/python_package_test/test_dask.py
+++ b/tests/python_package_test/test_dask.py
@@ -1451,7 +1451,15 @@ def test_init_score(task, output, cluster, rng):
 
         model_factory = task_to_dask_factory[task]
 
-        params = {"n_estimators": 1, "num_leaves": 2, "time_out": 5}
+        params = {
+            "n_estimators": 1,
+            "num_leaves": 2,
+            "time_out": 5,
+            "seed": 708,
+            "deterministic": True,
+            "force_row_wise": True,
+            "num_thread": 1,
+        }
         num_classes = 1
         if task == "multiclass-classification":
             num_classes = 3
@@ -1533,6 +1541,43 @@ def test_predict_with_raw_score(task, output, cluster):
             assert_eq(raw_predictions, pred_proba_raw)
 
 
+@pytest.mark.parametrize("output", data_output)
+@pytest.mark.parametrize("use_init_score", [False, True])
+def test_predict_stump(output, use_init_score, cluster, rng):
+    with Client(cluster) as client:
+        task = "binary-classification"
+        n_samples = 1_000
+        _, _, _, _, dX, dy, _, dg = _create_data(objective=task, n_samples=n_samples, output=output)
+
+        model_factory = task_to_dask_factory[task]
+
+        params = {"objective": "binary", "n_estimators": 5, "min_data_in_leaf": n_samples}
+
+        if not use_init_score:
+            init_scores = None
+        elif output.startswith("dataframe"):
+            init_scores = dy.map_partitions(lambda x: pd.DataFrame(rng.uniform(size=x.size)))
+        else:
+            init_scores = dy.map_blocks(lambda x: rng.uniform(size=x.size))
+
+        model = model_factory(client=client, **params)
+        model.fit(dX, dy, group=dg, init_score=init_scores)
+        preds_1 = model.predict(dX, raw_score=True, num_iteration=1).compute()
+        preds_all = model.predict(dX, raw_score=True).compute()
+
+        if use_init_score:
+            # if init_score was provided, a model of stumps should predict all 0s
+            all_zeroes = np.full_like(preds_1, fill_value=0.0)
+            assert_eq(preds_1, all_zeroes)
+            assert_eq(preds_all, all_zeroes)
+        else:
+            # if init_score was not provided, prediction for a model of stumps should be
+            # the "average" of the labels
+            y_avg = np.log(dy.mean() / (1.0 - dy.mean()))
+            assert_eq(preds_1, np.full_like(preds_1, fill_value=y_avg))
+            assert_eq(preds_all, np.full_like(preds_all, fill_value=y_avg))
+
+
 def test_distributed_quantized_training(tmp_path, cluster):
     with Client(cluster) as client:
         X, y, w, _, dX, dy, dw, _ = _create_data(objective="regression", output="array")