diff --git a/grep.c b/grep.c
index 451275d298..627ae3e3e8 100644
--- a/grep.c
+++ b/grep.c
@@ -5,6 +5,7 @@
 #include "diff.h"
 #include "diffcore.h"
 #include "commit.h"
+#include "quote.h"
 
 static int grep_source_load(struct grep_source *gs);
 static int grep_source_is_binary(struct grep_source *gs);
@@ -397,6 +398,28 @@ static int is_fixed(const char *s, size_t len)
 	return 1;
 }
 
+static void compile_fixed_regexp(struct grep_pat *p, struct grep_opt *opt)
+{
+	struct strbuf sb = STRBUF_INIT;
+	int err;
+	int regflags;
+
+	basic_regex_quote_buf(&sb, p->pattern);
+	regflags = opt->regflags & ~REG_EXTENDED;
+	if (opt->ignore_case)
+		regflags |= REG_ICASE;
+	err = regcomp(&p->regexp, sb.buf, regflags);
+	if (opt->debug)
+		fprintf(stderr, "fixed %s\n", sb.buf);
+	strbuf_release(&sb);
+	if (err) {
+		char errbuf[1024];
+		regerror(err, &p->regexp, errbuf, sizeof(errbuf));
+		regfree(&p->regexp);
+		compile_regexp_failed(p, errbuf);
+	}
+}
+
 static void compile_regexp(struct grep_pat *p, struct grep_opt *opt)
 {
 	int icase, ascii_only;
@@ -407,8 +430,20 @@ static void compile_regexp(struct grep_pat *p, struct grep_opt *opt)
 	icase	       = opt->regflags & REG_ICASE || p->ignore_case;
 	ascii_only     = !has_non_ascii(p->pattern);
 
+	/*
+	 * Even when -F (fixed) asks us to do a non-regexp search, we
+	 * may not be able to correctly case-fold when -i
+	 * (ignore-case) is asked (in which case, we'll synthesize a
+	 * regexp to match the pattern that matches regexp special
+	 * characters literally, while ignoring case differences).  On
+	 * the other hand, even without -F, if the pattern does not
+	 * have any regexp special characters and there is no need for
+	 * case-folding search, we can internally turn it into a
+	 * simple string match using kws.  p->fixed tells us if we
+	 * want to use kws.
+	 */
 	if (opt->fixed)
-		p->fixed = 1;
+		p->fixed = !icase || ascii_only;
 	else if ((!icase || ascii_only) &&
 		 is_fixed(p->pattern, p->patternlen))
 		p->fixed = 1;
@@ -423,6 +458,14 @@ static void compile_regexp(struct grep_pat *p, struct grep_opt *opt)
 		kwsincr(p->kws, p->pattern, p->patternlen);
 		kwsprep(p->kws);
 		return;
+	} else if (opt->fixed) {
+		/*
+		 * We come here when the pattern has the non-ascii
+		 * characters we cannot case-fold, and asked to
+		 * ignore-case.
+		 */
+		compile_fixed_regexp(p, opt);
+		return;
 	}
 
 	if (opt->pcre) {
diff --git a/quote.c b/quote.c
index fe884d2452..c67adb718c 100644
--- a/quote.c
+++ b/quote.c
@@ -440,3 +440,40 @@ void tcl_quote_buf(struct strbuf *sb, const char *src)
 	}
 	strbuf_addch(sb, '"');
 }
+
+void basic_regex_quote_buf(struct strbuf *sb, const char *src)
+{
+	char c;
+
+	if (*src == '^') {
+		/* only beginning '^' is special and needs quoting */
+		strbuf_addch(sb, '\\');
+		strbuf_addch(sb, *src++);
+	}
+	if (*src == '*')
+		/* beginning '*' is not special, no quoting */
+		strbuf_addch(sb, *src++);
+
+	while ((c = *src++)) {
+		switch (c) {
+		case '[':
+		case '.':
+		case '\\':
+		case '*':
+			strbuf_addch(sb, '\\');
+			strbuf_addch(sb, c);
+			break;
+
+		case '$':
+			/* only the end '$' is special and needs quoting */
+			if (*src == '\0')
+				strbuf_addch(sb, '\\');
+			strbuf_addch(sb, c);
+			break;
+
+		default:
+			strbuf_addch(sb, c);
+			break;
+		}
+	}
+}
diff --git a/quote.h b/quote.h
index 99e04d34bf..362d315bec 100644
--- a/quote.h
+++ b/quote.h
@@ -67,5 +67,6 @@ extern char *quote_path_relative(const char *in, const char *prefix,
 extern void perl_quote_buf(struct strbuf *sb, const char *src);
 extern void python_quote_buf(struct strbuf *sb, const char *src);
 extern void tcl_quote_buf(struct strbuf *sb, const char *src);
+extern void basic_regex_quote_buf(struct strbuf *sb, const char *src);
 
 #endif
diff --git a/t/t7812-grep-icase-non-ascii.sh b/t/t7812-grep-icase-non-ascii.sh
index b78a774dab..1929809d4a 100755
--- a/t/t7812-grep-icase-non-ascii.sh
+++ b/t/t7812-grep-icase-non-ascii.sh
@@ -20,4 +20,30 @@ test_expect_success REGEX_LOCALE 'grep literal string, no -F' '
 	git grep -i "TILRAUN: HALLÓ HEIMUR!"
 '
 
+test_expect_success REGEX_LOCALE 'grep literal string, with -F' '
+	git grep --debug -i -F "TILRAUN: Halló Heimur!"  2>&1 >/dev/null |
+		 grep fixed >debug1 &&
+	test_write_lines "fixed TILRAUN: Halló Heimur!" >expect1 &&
+	test_cmp expect1 debug1 &&
+
+	git grep --debug -i -F "TILRAUN: HALLÓ HEIMUR!"  2>&1 >/dev/null |
+		 grep fixed >debug2 &&
+	test_write_lines "fixed TILRAUN: HALLÓ HEIMUR!" >expect2 &&
+	test_cmp expect2 debug2
+'
+
+test_expect_success REGEX_LOCALE 'grep string with regex, with -F' '
+	test_write_lines "^*TILR^AUN:.* \\Halló \$He[]imur!\$" >file &&
+
+	git grep --debug -i -F "^*TILR^AUN:.* \\Halló \$He[]imur!\$" 2>&1 >/dev/null |
+		 grep fixed >debug1 &&
+	test_write_lines "fixed \\^*TILR^AUN:\\.\\* \\\\Halló \$He\\[]imur!\\\$" >expect1 &&
+	test_cmp expect1 debug1 &&
+
+	git grep --debug -i -F "^*TILR^AUN:.* \\HALLÓ \$HE[]IMUR!\$"  2>&1 >/dev/null |
+		 grep fixed >debug2 &&
+	test_write_lines "fixed \\^*TILR^AUN:\\.\\* \\\\HALLÓ \$HE\\[]IMUR!\\\$" >expect2 &&
+	test_cmp expect2 debug2
+'
+
 test_done