diff --git a/Modules/Core/Common/test/itkPointSetGTest.cxx b/Modules/Core/Common/test/itkPointSetGTest.cxx
index 6c1cb8f2ea5..8461daae77a 100644
--- a/Modules/Core/Common/test/itkPointSetGTest.cxx
+++ b/Modules/Core/Common/test/itkPointSetGTest.cxx
@@ -18,6 +18,7 @@
 
 // First include the header file to be tested:
 #include "itkPointSet.h"
+#include "itkDeref.h"
 #include "../../QuadEdgeMesh/include/itkQuadEdgeMeshTraits.h"
 #include <gtest/gtest.h>
 #include <algorithm> // For equal.
@@ -80,3 +81,36 @@ TEST(PointSet, SetPointsByCoordinates)
   TestSetPointsByCoordinates(*itk::PointSet<int>::New());
   TestSetPointsByCoordinates(*itk::PointSet<double, 2, itk::QuadEdgeMeshTraits<double, 2, bool, bool>>::New());
 }
+
+
+// Tests that PointSet::Graft copies the pointers to the points and the data.
+TEST(PointSet, GraftDoesShallowCopyOfPointsAndData)
+{
+  const auto check = [](const auto & pointSet) {
+    const auto clone = pointSet.Clone();
+
+    // Check that Clone() did not return null, by using itk::Deref(ptr).
+    const auto & constClone = itk::Deref(clone.get());
+
+    clone->Graft(&pointSet);
+
+    // Expect that Graft does "shallow copying", only copying the *pointers* to the points and the data.
+    EXPECT_EQ(constClone.GetPoints(), pointSet.GetPoints());
+    EXPECT_EQ(constClone.GetPointData(), pointSet.GetPointData());
+  };
+
+  // First check an empty point set:
+  check(*itk::PointSet<int>::New());
+
+  // Then check a non-empty point set with `double` data:
+  using PixelType = double;
+  static constexpr unsigned int Dimension = 2;
+  using PointSetType = itk::PointSet<PixelType, Dimension>;
+  using PointType = PointSetType::PointType;
+
+  const auto pointSet = PointSetType::New();
+  pointSet->SetPoints(itk::MakeVectorContainer<PointType>({ PointType(), itk::MakeFilled<PointType>(1.0f) }));
+  pointSet->SetPointData(itk::MakeVectorContainer<PixelType>({ 0.0, 1.0, 2.0 }));
+
+  check(*pointSet);
+}