diff --git a/Lib/fontTools/ttLib/reorderGlyphs.py b/Lib/fontTools/ttLib/reorderGlyphs.py
index 3221261f1..fd950ba0e 100644
--- a/Lib/fontTools/ttLib/reorderGlyphs.py
+++ b/Lib/fontTools/ttLib/reorderGlyphs.py
@@ -19,9 +19,7 @@ from typing import (
     Deque,
     Iterable,
     List,
-    NamedTuple,
     Tuple,
-    Union,
 )
 
 
@@ -276,3 +274,11 @@ def reorderGlyphs(font: ttLib.TTFont, new_glyph_order: List[str]):
                 reorder_key = (type(value), getattr(value, "Format", None))
                 for reorder in _REORDER_RULES.get(reorder_key, []):
                     reorder.apply(font, value)
+
+    if "CFF " in font:
+        cff_table = font["CFF "]
+        charstrings = cff_table.cff.topDictIndex[0].CharStrings.charStrings
+        cff_table.cff.topDictIndex[0].charset = new_glyph_order
+        cff_table.cff.topDictIndex[0].CharStrings.charStrings = {
+            k: charstrings.get(k) for k in new_glyph_order
+        }
diff --git a/Tests/ttLib/reorderGlyphs_test.py b/Tests/ttLib/reorderGlyphs_test.py
index cfda2d285..02ac2f49d 100644
--- a/Tests/ttLib/reorderGlyphs_test.py
+++ b/Tests/ttLib/reorderGlyphs_test.py
@@ -59,6 +59,17 @@ def test_ttfont_reorder_glyphs():
     assert list(reversed(old_coverage2)) == new_coverage2
 
 
+def test_reorder_glyphs_cff():
+    font_path = DATA_DIR / "TestVGID-Regular.otf"
+    font = TTFont(str(font_path))
+    ga = font.getGlyphOrder()
+    ga = list(reversed(ga))
+    reorderGlyphs(font, ga)
+
+    assert list(font["CFF "].cff.topDictIndex[0].CharStrings.charStrings.keys()) == ga
+    assert font["CFF "].cff.topDictIndex[0].charset == ga
+
+
 def test_reorder_glyphs_bad_length(caplog):
     font_path = DATA_DIR / "Test-Regular.ttf"
     font = TTFont(str(font_path))