diff --git a/Lib/gzip.py b/Lib/gzip.py
index 7c3fd5157e7..21b140498f8 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -210,6 +210,13 @@ class GzipFile(io.BufferedIOBase):
         s = repr(fileobj)
         return '<gzip ' + s[1:-1] + ' ' + hex(id(self)) + '>'
 
+    def _check_closed(self):
+        """Raises a ValueError if the underlying file object has been closed.
+
+        """
+        if self.closed:
+            raise ValueError('I/O operation on closed file.')
+
     def _init_write(self, filename):
         self.name = filename
         self.crc = zlib.crc32(b"") & 0xffffffff
@@ -288,6 +295,7 @@ class GzipFile(io.BufferedIOBase):
             self._add_read_data(uncompress)
 
     def write(self,data):
+        self._check_closed()
         if self.mode != WRITE:
             import errno
             raise IOError(errno.EBADF, "write() on read-only GzipFile object")
@@ -308,6 +316,7 @@ class GzipFile(io.BufferedIOBase):
         return len(data)
 
     def read(self, size=-1):
+        self._check_closed()
         if self.mode != READ:
             import errno
             raise IOError(errno.EBADF, "read() on write-only GzipFile object")
@@ -457,6 +466,7 @@ class GzipFile(io.BufferedIOBase):
             self.myfileobj = None
 
     def flush(self,zlib_mode=zlib.Z_SYNC_FLUSH):
+        self._check_closed()
         if self.mode == WRITE:
             # Ensure the compressor's buffer is flushed
             self.fileobj.write(self.compress.flush(zlib_mode))
diff --git a/Lib/test/test_gzip.py b/Lib/test/test_gzip.py
index 8e493b50000..4a364c21994 100644
--- a/Lib/test/test_gzip.py
+++ b/Lib/test/test_gzip.py
@@ -62,6 +62,28 @@ class TestGzip(unittest.TestCase):
         f = gzip.GzipFile(self.filename, 'r') ; d = f.read() ; f.close()
         self.assertEqual(d, data1*50)
 
+    def test_io_on_closed_object(self):
+        # Test that I/O operations on closed GzipFile objects raise a
+        # ValueError, just like the corresponding functions on file objects.
+
+        # Write to a file, open it for reading, then close it.
+        self.test_write()
+        f = gzip.GzipFile(self.filename, 'r')
+        f.close()
+        with self.assertRaises(ValueError):
+            f.read(1)
+        with self.assertRaises(ValueError):
+            f.seek(0)
+        with self.assertRaises(ValueError):
+            f.tell()
+        # Open the file for writing, then close it.
+        f = gzip.GzipFile(self.filename, 'w')
+        f.close()
+        with self.assertRaises(ValueError):
+            f.write(b'')
+        with self.assertRaises(ValueError):
+            f.flush()
+
     def test_append(self):
         self.test_write()
         # Append to the previous file
diff --git a/Misc/NEWS b/Misc/NEWS
index 7042774b672..e62dc77d493 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -88,6 +88,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #9759: GzipFile now raises ValueError when an operation is attempted
+  after the file is closed.  Patch by Jeffrey Finkelstein.
+
 - Issue #9042: Fix interaction of custom translation classes and caching in
   gettext.