diff --git a/src/metric/elementwise_metric.cu b/src/metric/elementwise_metric.cu
index 25492bf2c5f8..9ff0cf1419b2 100644
--- a/src/metric/elementwise_metric.cu
+++ b/src/metric/elementwise_metric.cu
@@ -309,8 +309,7 @@ struct EvalGammaNLogLik {
     float constexpr kPsi = 1.0;
     bst_float theta = -1. / py;
     bst_float a = kPsi;
-    // b = -std::log(-theta);
-    float b = 1.0f;
+    float b = -std::log(-theta);
     // c = 1. / kPsi * std::log(y/kPsi) - std::log(y) - common::LogGamma(1. / kPsi);
     //   = 1.0f      * std::log(y)      - std::log(y) - 0 = 0
     float c = 0;
diff --git a/src/objective/regression_obj.cu b/src/objective/regression_obj.cu
index ccb3a723d32e..43c27ab064eb 100644
--- a/src/objective/regression_obj.cu
+++ b/src/objective/regression_obj.cu
@@ -421,7 +421,7 @@ class GammaRegression : public ObjFunction {
           bst_float p = _preds[_idx];
           bst_float w = is_null_weight ? 1.0f : _weights[_idx];
           bst_float y = _labels[_idx];
-          if (y <= 0.0f) {
+          if (y < 0.0f) {
             _label_correct[0] = 0;
           }
           _out_gpair[_idx] = GradientPair((1 - y / expf(p)) * w, y / expf(p) * w);
@@ -433,7 +433,7 @@ class GammaRegression : public ObjFunction {
     std::vector<int>& label_correct_h = label_correct_.HostVector();
     for (auto const flag : label_correct_h) {
       if (flag == 0) {
-        LOG(FATAL) << "GammaRegression: label must be positive.";
+        LOG(FATAL) << "GammaRegression: label must be non-negative.";
       }
     }
   }