diff --git a/lib/matplotlib/backends/backend_gtk3agg.py b/lib/matplotlib/backends/backend_gtk3agg.py
index f54849cf049c..c7b79c75a109 100644
--- a/lib/matplotlib/backends/backend_gtk3agg.py
+++ b/lib/matplotlib/backends/backend_gtk3agg.py
@@ -1,6 +1,8 @@
-import numpy as np
+import sys
 import warnings
 
+import numpy as np
+
 from . import backend_agg, backend_cairo, backend_gtk3
 from ._gtk3_compat import gi
 from .backend_cairo import cairo
@@ -31,7 +33,7 @@ def _render_figure(self, width, height):
         backend_agg.FigureCanvasAgg.draw(self)
 
     def on_draw_event(self, widget, ctx):
-        """ GtkDrawable draw event, like expose_event in GTK 2.X
+        """GtkDrawable draw event, like expose_event in GTK 2.X.
         """
         allocation = self.get_allocation()
         w, h = allocation.width, allocation.height
@@ -45,17 +47,29 @@ def on_draw_event(self, widget, ctx):
         ctx = backend_cairo._to_context(ctx)
 
         for bbox in bbox_queue:
-            area = self.copy_from_bbox(bbox)
-            buf = np.fromstring(area.to_string_argb(), dtype='uint8')
-
             x = int(bbox.x0)
             y = h - int(bbox.y1)
             width = int(bbox.x1) - int(bbox.x0)
             height = int(bbox.y1) - int(bbox.y0)
 
+            buf = (np.fromstring(self.copy_from_bbox(bbox).to_string_argb(),
+                                 dtype='uint8')
+                   .reshape((width, height, 4)))
+            # cairo wants premultiplied alpha.  Only bother doing the
+            # conversion when the alpha channel is not fully opaque, as the
+            # cost is not negligible.  (The unsafe cast is needed to do the
+            # multiplication in-place in an integer buffer.)
+            if sys.byteorder == "little":
+                rgb24 = buf[..., :-1]
+                alpha8 = buf[..., -1:]
+            else:
+                alpha8 = buf[..., :1]
+                rgb24 = buf[..., 1:]
+            if alpha8.min() != 0xff:
+                np.multiply(rgb24, alpha8 / 0xff, out=rgb24, casting="unsafe")
+
             image = cairo.ImageSurface.create_for_data(
-                buf.ravel().data, cairo.FORMAT_ARGB32,
-                width, height, width * 4)
+                buf.ravel().data, cairo.FORMAT_ARGB32, width, height)
             ctx.set_source_surface(image, x, y)
             ctx.paint()