diff --git a/gnu/local.mk b/gnu/local.mk
index 79d6b14a2b..00f47e3165 100644
--- a/gnu/local.mk
+++ b/gnu/local.mk
@@ -857,6 +857,7 @@ dist_patch_DATA =						\
   %D%/packages/patches/t1lib-CVE-2010-2642.patch		\
   %D%/packages/patches/t1lib-CVE-2011-0764.patch		\
   %D%/packages/patches/t1lib-CVE-2011-1552+CVE-2011-1553+CVE-2011-1554.patch		\
+  %D%/packages/patches/tar-CVE-2016-6321.patch			\
   %D%/packages/patches/tar-skip-unreliable-tests.patch		\
   %D%/packages/patches/tcl-mkindex-deterministic.patch		\
   %D%/packages/patches/tclxml-3.2-install.patch			\
diff --git a/gnu/packages/base.scm b/gnu/packages/base.scm
index 30364f373c..1962086169 100644
--- a/gnu/packages/base.scm
+++ b/gnu/packages/base.scm
@@ -162,7 +162,8 @@ implementation offers several extensions over the standard utility.")
             (sha256
              (base32
               "097hx7sbzp8qirl4m930lw84kn0wmxhmq7v1qpra3mrg0b8cyba0"))
-            (patches (search-patches "tar-skip-unreliable-tests.patch"))))
+            (patches (search-patches "tar-CVE-2016-6321.patch"
+                                     "tar-skip-unreliable-tests.patch"))))
    (build-system gnu-build-system)
    ;; Note: test suite requires ~1GiB of disk space.
    (arguments
diff --git a/gnu/packages/patches/tar-CVE-2016-6321.patch b/gnu/packages/patches/tar-CVE-2016-6321.patch
new file mode 100644
index 0000000000..b79be9bc94
--- /dev/null
+++ b/gnu/packages/patches/tar-CVE-2016-6321.patch
@@ -0,0 +1,51 @@
+Fix CVE-2016-6321:
+
+https://cve.mitre.org/cgi-bin/cvename.cgi?name=CVE-2016-6321
+https://security-tracker.debian.org/tracker/CVE-2016-6321
+
+Patch adapted from upstream source repository (the changes to 'NEWS'
+don't apply to the Tar 1.29 release tarball).
+
+http://git.savannah.gnu.org/cgit/tar.git/commit/?id=7340f67b9860ea0531c1450e5aa261c50f67165d
+
+From 7340f67b9860ea0531c1450e5aa261c50f67165d Mon Sep 17 00:00:00 2001
+From: Paul Eggert <eggert@Penguin.CS.UCLA.EDU>
+Date: Sat, 29 Oct 2016 21:04:40 -0700
+Subject: [PATCH] When extracting, skip ".." members
+
+* NEWS: Document this.
+* src/extract.c (extract_archive): Skip members whose names
+contain "..".
+---
+ NEWS          | 8 +++++++-
+ src/extract.c | 8 ++++++++
+ 2 files changed, 15 insertions(+), 1 deletion(-)
+
+diff --git a/src/extract.c b/src/extract.c
+index f982433..7904148 100644
+--- a/src/extract.c
++++ b/src/extract.c
+@@ -1629,12 +1629,20 @@ extract_archive (void)
+ {
+   char typeflag;
+   tar_extractor_t fun;
++  bool skip_dotdot_name;
+ 
+   fatal_exit_hook = extract_finish;
+ 
+   set_next_block_after (current_header);
+ 
++  skip_dotdot_name = (!absolute_names_option
++		      && contains_dot_dot (current_stat_info.orig_file_name));
++  if (skip_dotdot_name)
++    ERROR ((0, 0, _("%s: Member name contains '..'"),
++	    quotearg_colon (current_stat_info.orig_file_name)));
++
+   if (!current_stat_info.file_name[0]
++      || skip_dotdot_name
+       || (interactive_option
+ 	  && !confirm ("extract", current_stat_info.file_name)))
+     {
+-- 
+2.11.0
+