diff --git a/arch-x86-64.cc b/arch-x86-64.cc
index 938f519c..4873adbc 100644
--- a/arch-x86-64.cc
+++ b/arch-x86-64.cc
@@ -410,7 +410,7 @@ void InputSection<X86_64>::apply_reloc_alloc(Context<X86_64> &ctx, u8 *base) {
       write(sym.esym().st_size + A);
       continue;
     case R_X86_64_TLSDESC_CALL:
-      if (ctx.arg.relax && !ctx.arg.shared) {
+      if (ctx.arg.is_static || (ctx.arg.relax && !ctx.arg.shared)) {
         // call *(%rax) -> nop
         loc[0] = 0x66;
         loc[1] = 0x90;
@@ -644,7 +644,10 @@ void InputSection<X86_64>::scan_relocations(Context<X86_64> &ctx) {
         Fatal(ctx) << *this << ": GOTPC32_TLSDESC relocation is used"
                    << " against an invalid code sequence";
 
-      if (!ctx.arg.relax || ctx.arg.shared)
+      // TLSDESC relocs must be relaxed for a statically-linked executable
+      // even if -no-relax is given. It is because a statically-linked
+      // executable doesn't contain a tranpoline function needed for TLSDESC.
+      if (!ctx.arg.is_static && (!ctx.arg.relax || ctx.arg.shared))
         sym.flags |= NEEDS_TLSDESC;
       break;
     case R_X86_64_TPOFF32:
diff --git a/test/tlsdesc-static.sh b/test/tlsdesc-static.sh
new file mode 100755
index 00000000..eb084913
--- /dev/null
+++ b/test/tlsdesc-static.sh
@@ -0,0 +1,39 @@
+#!/bin/bash
+set -e
+cd $(dirname $0)
+mold=`pwd`/../mold
+echo -n "Testing $(basename -s .sh $0) ... "
+t=$(pwd)/tmp/$(basename -s .sh $0)
+mkdir -p $t
+
+if [ $(uname -m) = x86_64 ]; then
+  dialect=gnu2
+elif [ $(uname -m) = aarch64 ]; then
+  dialect=desc
+else
+  echo skipped
+  exit 0
+fi
+
+cat <<EOF | gcc -fPIC -mtls-dialect=$dialect -c -o $t/a.o -xc -
+#include <stdio.h>
+
+extern _Thread_local int foo;
+
+int main() {
+  foo = 42;
+  printf("%d\n", foo);
+}
+EOF
+
+cat <<EOF | gcc -fPIC -mtls-dialect=$dialect -c -o $t/b.o -xc -
+_Thread_local int foo;
+EOF
+
+clang -fuse-ld=$mold -o $t/exe $t/a.o $t/b.o -static
+$t/exe | grep -q 42
+
+clang -fuse-ld=$mold -o $t/exe $t/a.o $t/b.o -static -Wl,-no-relax
+$t/exe | grep -q 42
+
+echo OK