diff --git a/builtin/check-ref-format.c b/builtin/check-ref-format.c
index ae3f28115..0723cf245 100644
--- a/builtin/check-ref-format.c
+++ b/builtin/check-ref-format.c
@@ -12,8 +12,8 @@ static const char builtin_check_ref_format_usage[] =
 "   or: git check-ref-format --branch <branchname-shorthand>";
 
 /*
- * Replace each run of adjacent slashes in src with a single slash,
- * and write the result to dst.
+ * Remove leading slashes and replace each run of adjacent slashes in
+ * src with a single slash, and write the result to dst.
  *
  * This function is similar to normalize_path_copy(), but stripped down
  * to meet check_ref_format's simpler needs.
@@ -21,7 +21,7 @@ static const char builtin_check_ref_format_usage[] =
 static void collapse_slashes(char *dst, const char *src)
 {
 	char ch;
-	char prev = '\0';
+	char prev = '/';
 
 	while ((ch = *src++) != '\0') {
 		if (prev == '/' && ch == prev)
diff --git a/t/t1402-check-ref-format.sh b/t/t1402-check-ref-format.sh
index 1b0f82fa4..7563043c5 100755
--- a/t/t1402-check-ref-format.sh
+++ b/t/t1402-check-ref-format.sh
@@ -18,6 +18,9 @@ invalid_ref 'foo'
 valid_ref 'foo/bar/baz'
 valid_ref 'refs///heads/foo'
 invalid_ref 'heads/foo/'
+valid_ref '/heads/foo'
+valid_ref '///heads/foo'
+invalid_ref '/foo'
 invalid_ref './foo'
 invalid_ref '.refs/foo'
 invalid_ref 'heads/foo..bar'
@@ -70,7 +73,10 @@ invalid_ref_normalized() {
 
 valid_ref_normalized 'heads/foo' 'heads/foo'
 valid_ref_normalized 'refs///heads/foo' 'refs/heads/foo'
+valid_ref_normalized '/heads/foo' 'heads/foo'
+valid_ref_normalized '///heads/foo' 'heads/foo'
 invalid_ref_normalized 'foo'
+invalid_ref_normalized '/foo'
 invalid_ref_normalized 'heads/foo/../bar'
 invalid_ref_normalized 'heads/./foo'
 invalid_ref_normalized 'heads\foo'