diff --git a/PIL/Image.py b/PIL/Image.py
index 1e29db198..cafc5a22f 100644
--- a/PIL/Image.py
+++ b/PIL/Image.py
@@ -713,6 +713,16 @@ class Image:
         if dither is None:
             dither = FLOYDSTEINBERG
 
+        # fake a P-mode image, otherwise the transparency will get lost as there is
+        # currently no other way to convert transparency into an RGBA image
+        if self.mode == "L" and mode == "RGBA" and "transparency" in self.info:
+            from PIL import ImagePalette
+            self.mode = "P"
+            bytePalette = bytes([i//3 for i in range(768)])
+            self.palette = ImagePalette.raw("RGB", bytePalette)
+            self.palette.dirty = 1
+            self.load()
+
         try:
             im = self.im.convert(mode, dither)
         except ValueError: