diff --git a/Tests/test_image_point.py b/Tests/test_image_point.py
index 366f45854..428ad116b 100644
--- a/Tests/test_image_point.py
+++ b/Tests/test_image_point.py
@@ -10,6 +10,7 @@ def test_sanity():
         im.point(list(range(256)))
     im.point(list(range(256)) * 3)
     im.point(lambda x: x)
+    im.point(lambda x: x * 1.2)
 
     im = im.convert("I")
     with pytest.raises(ValueError):
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index aa7e3c2e6..ab391b9b4 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -1720,6 +1720,8 @@ class Image:
             # FIXME: _imaging returns a confusing error message for this case
             raise ValueError("point operation not supported for this mode")
 
+        if mode != "F":
+            lut = [round(i) for i in lut]
         return self._new(self.im.point(lut, mode))
 
     def putalpha(self, alpha):