diff --git a/builtin/rm.c b/builtin/rm.c
index 2aea3b5653..dabfcf6890 100644
--- a/builtin/rm.c
+++ b/builtin/rm.c
@@ -234,6 +234,21 @@ int cmd_rm(int argc, const char **argv, const char *prefix)
 	if (read_cache() < 0)
 		die(_("index file corrupt"));
 
+	/*
+	 * Drop trailing directory separators from directories so we'll find
+	 * submodules in the index.
+	 */
+	for (i = 0; i < argc; i++) {
+		size_t pathlen = strlen(argv[i]);
+		if (pathlen && is_dir_sep(argv[i][pathlen - 1]) &&
+		    is_directory(argv[i])) {
+			do {
+				pathlen--;
+			} while (pathlen && is_dir_sep(argv[i][pathlen - 1]));
+			argv[i] = xmemdupz(argv[i], pathlen);
+		}
+	}
+
 	pathspec = get_pathspec(prefix, argv);
 	refresh_index(&the_index, REFRESH_QUIET, pathspec, NULL, NULL);
 
diff --git a/t/t3600-rm.sh b/t/t3600-rm.sh
index 97254e8d33..06f63848ea 100755
--- a/t/t3600-rm.sh
+++ b/t/t3600-rm.sh
@@ -302,6 +302,23 @@ test_expect_success 'rm removes work tree of unmodified submodules' '
 	test_cmp expect actual
 '
 
+test_expect_success 'rm removes a submodule with a trailing /' '
+	git reset --hard &&
+	git submodule update &&
+	git rm submod/ &&
+	test ! -d submod &&
+	git status -s -uno --ignore-submodules=none > actual &&
+	test_cmp expect actual
+'
+
+test_expect_success 'rm fails when given a file with a trailing /' '
+	test_must_fail git rm empty/
+'
+
+test_expect_success 'rm succeeds when given a directory with a trailing /' '
+	git rm -r frotz/
+'
+
 test_expect_success 'rm of a populated submodule with different HEAD fails unless forced' '
 	git reset --hard &&
 	git submodule update &&