diff --git a/Tests/images/pal8_offset.bmp b/Tests/images/pal8_offset.bmp
new file mode 100644
index 00000000000..24be65f22c3
Binary files /dev/null and b/Tests/images/pal8_offset.bmp differ
diff --git a/Tests/test_file_bmp.py b/Tests/test_file_bmp.py
index 3374fe54e94..47fc97df055 100644
--- a/Tests/test_file_bmp.py
+++ b/Tests/test_file_bmp.py
@@ -123,3 +123,10 @@ def test_rgba_bitfields():
         im = Image.merge("RGB", (r, g, b))
 
     assert_image_equal_tofile(im, "Tests/images/bmp/q/rgb32bf-xbgr.bmp")
+
+
+def test_offset():
+    # This image has been hexedited
+    # to exclude the palette size from the pixel data offset
+    with Image.open("Tests/images/pal8_offset.bmp") as im:
+        assert_image_equal_tofile(im, "Tests/images/bmp/g/pal8.bmp")
diff --git a/src/PIL/BmpImagePlugin.py b/src/PIL/BmpImagePlugin.py
index 7bfe733e52d..7a7ad386c6f 100644
--- a/src/PIL/BmpImagePlugin.py
+++ b/src/PIL/BmpImagePlugin.py
@@ -158,6 +158,8 @@ def _bitmap(self, header=0, offset=0):
             if file_info.get("colors", 0)
             else (1 << file_info["bits"])
         )
+        if offset == 14 + file_info["header_size"] and file_info["bits"] <= 8:
+            offset += 4 * file_info["colors"]
 
         # ---------------------- Check bit depth for unusual unsupported values
         self.mode, raw_mode = BIT2MODE.get(file_info["bits"], (None, None))