diff --git a/Lib/fontTools/ttLib/woff2.py b/Lib/fontTools/ttLib/woff2.py
index 02e273d2e..3e247b02e 100644
--- a/Lib/fontTools/ttLib/woff2.py
+++ b/Lib/fontTools/ttLib/woff2.py
@@ -1041,6 +1041,8 @@ class WOFF2GlyfTable(getTableClass("glyf")):
 
     def _encodeCoordinates(self, glyph):
         lastEndPoint = -1
+        if _g_l_y_f.flagCubic in glyph.flags:
+            raise NotImplementedError
         for endPoint in glyph.endPtsOfContours:
             ptsOfContour = endPoint - lastEndPoint
             self.nPointsStream += pack255UShort(ptsOfContour)
diff --git a/Tests/ttLib/woff2_test.py b/Tests/ttLib/woff2_test.py
index 0a89b8b43..e098eb993 100644
--- a/Tests/ttLib/woff2_test.py
+++ b/Tests/ttLib/woff2_test.py
@@ -28,6 +28,7 @@ from fontTools.misc import sstruct
 from fontTools.misc.textTools import Tag, bytechr, byteord
 from fontTools import fontBuilder
 from fontTools.pens.ttGlyphPen import TTGlyphPen
+from fontTools.pens.recordingPen import RecordingPen
 from io import BytesIO
 import struct
 import os
@@ -1505,6 +1506,28 @@ class VarCompositeTest(unittest.TestCase):
         ttf.save(out)
 
 
+class CubicTest(unittest.TestCase):
+    def test_cubic(self):
+        input_path = os.path.join(
+            data_dir, "..", "tables", "data", "NotoSans-VF-cubic.subset.ttf"
+        )
+        ttf = ttLib.TTFont(input_path)
+        pen1 = RecordingPen()
+        ttf.getGlyphSet()["a"].draw(pen1)
+        ttf.flavor = "woff2"
+        out = BytesIO()
+        ttf.save(out)
+
+        ttf = ttLib.TTFont(out)
+        ttf.flavor = None
+        pen2 = RecordingPen()
+        ttf.getGlyphSet()["a"].draw(pen2)
+        out = BytesIO()
+        ttf.save(out)
+
+        assert pen1.value == pen2.value
+
+
 if __name__ == "__main__":
     import sys