diff --git a/Doc/library/gzip.rst b/Doc/library/gzip.rst
index 1a2582d6a904b2..45670ced239173 100644
--- a/Doc/library/gzip.rst
+++ b/Doc/library/gzip.rst
@@ -173,6 +173,9 @@ The module defines the following items:
       Opening :class:`GzipFile` for writing without specifying the *mode*
       argument is deprecated.
 
+   .. versionchanged:: 3.11
+      A UserWarning is now emitted when gzip files contain trailing garbage
+      instead of throwing a BadGzipFile error.
 
 .. function:: compress(data, compresslevel=9, *, mtime=None)
 
@@ -202,6 +205,9 @@ The module defines the following items:
    .. versionchanged:: 3.11
       Speed is improved by decompressing members at once in memory instead of in
       a streamed fashion.
+   .. versionchanged:: 3.11
+      A UserWarning is now emitted when gzip data contains trailing garbage
+      instead of throwing a BadGzipFile error.
 
 .. _gzip-usage-examples:
 
diff --git a/Lib/gzip.py b/Lib/gzip.py
index 75c6ddc3f2cffb..8691aaedf6381d 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -9,6 +9,7 @@
 import zlib
 import builtins
 import io
+import warnings
 import _compression
 
 __all__ = ["BadGzipFile", "GzipFile", "open", "compress", "decompress"]
@@ -409,18 +410,22 @@ def _read_exact(fp, n):
     return data
 
 
-def _read_gzip_header(fp):
+def _read_gzip_header(fp, first_member=True):
     '''Read a gzip header from `fp` and progress to the end of the header.
 
-    Returns last mtime if header was present or None otherwise.
+    Returns last mtime if header was present or None otherwise. Raises an
+    error if the magic does not match the gzip magic, unless first_member is
+    False, in which case it only warns about trailing garbage.
     '''
     magic = fp.read(2)
     if magic == b'':
         return None
 
     if magic != b'\037\213':
-        raise BadGzipFile('Not a gzipped file (%r)' % magic)
-
+        if first_member:
+            raise BadGzipFile('Not a gzipped file (%r)' % magic)
+        warnings.warn("Trailing garbage in gzip data ignored.")
+        return None
     (method, flag, last_mtime) = struct.unpack("<BBIxx", _read_exact(fp, 8))
     if method != 8:
         raise BadGzipFile('Unknown compression method')
@@ -453,13 +458,15 @@ def __init__(self, fp):
         # Set flag indicating start of a new member
         self._new_member = True
         self._last_mtime = None
+        self._decompressed_members = 0
 
     def _init_read(self):
         self._crc = zlib.crc32(b"")
         self._stream_size = 0  # Decompressed size of unconcatenated stream
 
     def _read_gzip_header(self):
-        last_mtime = _read_gzip_header(self._fp)
+        last_mtime = _read_gzip_header(self._fp,
+                                       not self._decompressed_members)
         if last_mtime is None:
             return False
         self._last_mtime = last_mtime
@@ -529,6 +536,7 @@ def _read_eof(self):
                                                              hex(self._crc)))
         elif isize != (self._stream_size & 0xffffffff):
             raise BadGzipFile("Incorrect length of data produced")
+        self._decompressed_members += 1
 
         # Gzip files can be padded with zeroes and still have archives.
         # Consume all zero bytes and set the file position to the first
@@ -590,7 +598,7 @@ def decompress(data):
     decompressed_members = []
     while True:
         fp = io.BytesIO(data)
-        if _read_gzip_header(fp) is None:
+        if _read_gzip_header(fp, not decompressed_members) is None:
             return b"".join(decompressed_members)
         # Use a zlib raw deflate compressor
         do = zlib.decompressobj(wbits=-zlib.MAX_WBITS)
diff --git a/Lib/test/test_gzip.py b/Lib/test/test_gzip.py
index 6de413e5056ef0..c0184cd902bd43 100644
--- a/Lib/test/test_gzip.py
+++ b/Lib/test/test_gzip.py
@@ -579,6 +579,17 @@ def test_decompress_missing_trailer(self):
         compressed_data = gzip.compress(data1)
         self.assertRaises(EOFError, gzip.decompress, compressed_data[:-8])
 
+    def test_trailing_garbage_decompress(self):
+        compressed_data = gzip.compress(data1) + b"garbage"
+        self.assertWarns(UserWarning, gzip.decompress, compressed_data )
+
+    def test_trailing_garbage_gzipfile(self):
+        compressed_data = gzip.compress(data1) + b"garbage"
+        fileobj = io.BytesIO(compressed_data)
+        with gzip.GzipFile(fileobj=fileobj, mode="rb") as g:
+            with self.assertWarns(UserWarning):
+                g.read()
+
     def test_read_truncated(self):
         data = data1*50
         # Drop the CRC (4 bytes) and file size (4 bytes).
diff --git a/Misc/NEWS.d/next/Library/2021-11-29-16-26-28.bpo-24301.qIaUJB.rst b/Misc/NEWS.d/next/Library/2021-11-29-16-26-28.bpo-24301.qIaUJB.rst
new file mode 100644
index 00000000000000..c4e7a6a9e37d0f
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-11-29-16-26-28.bpo-24301.qIaUJB.rst
@@ -0,0 +1,2 @@
+A UserWarning is now emitted when gzip files contain trailing garbage
+instead of throwing a BadGzipFile error.