diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
index 87a5c1e64de7..46b8ac2d46ca 100644
--- a/lib/matplotlib/backends/backend_pdf.py
+++ b/lib/matplotlib/backends/backend_pdf.py
@@ -2591,7 +2591,8 @@ def print_pdf(self, filename, **kwargs):
                 bbox_inches_restore=_bbox_inches_restore)
             self.figure.draw(renderer)
             renderer.finalize()
-            file.finalize()
+            if not isinstance(filename, PdfPages):
+                file.finalize()
         finally:
             if isinstance(filename, PdfPages):  # finish off this page
                 file.endStream()
diff --git a/lib/matplotlib/tests/test_backend_pdf.py b/lib/matplotlib/tests/test_backend_pdf.py
index 7f1439f89cf3..965e7ef585fd 100644
--- a/lib/matplotlib/tests/test_backend_pdf.py
+++ b/lib/matplotlib/tests/test_backend_pdf.py
@@ -7,6 +7,7 @@
 
 import io
 import os
+import sys
 import tempfile
 
 import pytest
@@ -71,6 +72,19 @@ def test_multipage_pagecount():
         assert pdf.get_pagecount() == 2
 
 
+def test_multipage_properfinalize():
+    pdfio = io.BytesIO()
+    with PdfPages(pdfio) as pdf:
+        for i in range(10):
+            fig = plt.figure()
+            ax = fig.add_subplot(111)
+            ax.set_title('This is a long title')
+            fig.savefig(pdf, format="pdf")
+    pdfio.seek(0)
+    assert sum(b'startxref' in line for line in pdfio) == 1
+    assert sys.getsizeof(pdfio) < 40000
+
+
 def test_multipage_keep_empty():
     from matplotlib.backends.backend_pdf import PdfPages
     from tempfile import NamedTemporaryFile