diff --git a/tests/cpp/objective/test_regression_obj.cc b/tests/cpp/objective/test_regression_obj.cc
index b454cf065..871b90092 100644
--- a/tests/cpp/objective/test_regression_obj.cc
+++ b/tests/cpp/objective/test_regression_obj.cc
@@ -136,3 +136,39 @@ TEST(Objective, GammaRegressionBasic) {
     EXPECT_NEAR(preds[i], out_preds[i], 0.01);
   }
 }
+
+TEST(Objective, TweedieRegressionGPair) {
+  xgboost::ObjFunction * obj = xgboost::ObjFunction::Create("reg:tweedie");
+  std::vector<std::pair<std::string, std::string> > args;
+  args.push_back(std::make_pair("tweedie_variance_power", "1.1"));
+  obj->Configure(args);
+  CheckObjFunction(obj,
+                   {   0,  0.1,  0.9,    1, 0,  0.1,  0.9,    1},
+                   {   0,    0,    0,    0, 1,    1,    1,    1},
+                   {   1,    1,    1,    1, 1,    1,    1,    1},
+                   {   1, 1.09, 2.24, 2.45, 0, 0.10, 1.33, 1.55},
+                   {0.89, 0.98, 2.02, 2.21, 1, 1.08, 2.11, 2.30});
+}
+
+TEST(Objective, TweedieRegressionBasic) {
+  xgboost::ObjFunction * obj = xgboost::ObjFunction::Create("reg:tweedie");
+  std::vector<std::pair<std::string, std::string> > args;
+  obj->Configure(args);
+
+  // test label validation
+  EXPECT_ANY_THROW(CheckObjFunction(obj, {0}, {-1}, {1}, {0}, {0}))
+    << "Expected error when label < 0 for TweedieRegression";
+
+  // test ProbToMargin
+  EXPECT_NEAR(obj->ProbToMargin(0.1), 0.10, 0.01);
+  EXPECT_NEAR(obj->ProbToMargin(0.5), 0.5, 0.01);
+  EXPECT_NEAR(obj->ProbToMargin(0.9), 0.89, 0.01);
+
+  // test PredTransform
+  std::vector<xgboost::bst_float> preds = {0, 0.1, 0.5, 0.9, 1};
+  std::vector<xgboost::bst_float> out_preds = {1, 1.10, 1.64, 2.45, 2.71};
+  obj->PredTransform(&preds);
+  for (int i = 0; i < preds.size(); ++i) {
+    EXPECT_NEAR(preds[i], out_preds[i], 0.01);
+  }
+}