diff --git a/tests/qtest/virtio-scsi-test.c b/tests/qtest/virtio-scsi-test.c
index 1b7ecc1c8f..8ceb12aacd 100644
--- a/tests/qtest/virtio-scsi-test.c
+++ b/tests/qtest/virtio-scsi-test.c
@@ -200,6 +200,42 @@ static void test_unaligned_write_same(void *obj, void *data,
     qvirtio_scsi_pci_free(vs);
 }
 
+/* Test UNMAP with a large LBA, issue #345 */
+static void test_unmap_large_lba(void *obj, void *data,
+                                      QGuestAllocator *t_alloc)
+{
+    QVirtioSCSI *scsi = obj;
+    QVirtioSCSIQueues *vs;
+    const uint8_t unmap[VIRTIO_SCSI_CDB_SIZE] = {
+        0x42, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x18, 0x00
+    };
+
+    /*
+     * Default null-co device size is 2**30
+     * LBA 0x7fff is ~ 1/8 into device, with 4k blocks
+     * if check_lba_range incorrectly using 512 bytes, will trigger sense error
+     */
+    uint8_t unmap_params[0x18] = {
+        0x00, 0x16, /* unmap data length */
+        0x00, 0x10, /* unmap block descriptor data length */
+        0x00, 0x00, 0x00, 0x00, /* reserved */
+        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, /* LBA */
+        0x00, 0x00, 0x03, 0xff, /* sector count */
+        0x00, 0x00, 0x00, 0x00, /* reserved */
+    };
+    struct virtio_scsi_cmd_resp resp;
+
+    alloc = t_alloc;
+    vs = qvirtio_scsi_init(scsi->vdev);
+
+    virtio_scsi_do_command(vs, unmap, NULL, 0, unmap_params,
+                           sizeof(unmap_params), &resp);
+    g_assert_cmphex(resp.response, ==, 0);
+    g_assert_cmphex(resp.status, !=, CHECK_CONDITION);
+
+    qvirtio_scsi_pci_free(vs);
+}
+
 static void test_write_to_cdrom(void *obj, void *data,
                                 QGuestAllocator *t_alloc)
 {
@@ -293,6 +329,17 @@ static void *virtio_scsi_setup(GString *cmd_line, void *arg)
     return arg;
 }
 
+static void *virtio_scsi_setup_4k(GString *cmd_line, void *arg)
+{
+    g_string_append(cmd_line,
+                    " -drive file=blkdebug::null-co://,"
+                    "file.image.read-zeroes=on,"
+                    "if=none,id=dr1,format=raw "
+                    "-device scsi-hd,drive=dr1,lun=0,scsi-id=1"
+                    ",logical_block_size=4k,physical_block_size=4k");
+    return arg;
+}
+
 static void *virtio_scsi_setup_cd(GString *cmd_line, void *arg)
 {
     g_string_append(cmd_line,
@@ -323,6 +370,10 @@ static void register_virtio_scsi_test(void)
     qos_add_test("unaligned-write-same", "virtio-scsi",
                  test_unaligned_write_same, &opts);
 
+    opts.before = virtio_scsi_setup_4k;
+    qos_add_test("large-lba-unmap", "virtio-scsi",
+                 test_unmap_large_lba, &opts);
+
     opts.before = virtio_scsi_setup_cd;
     qos_add_test("write-to-cdrom", "virtio-scsi", test_write_to_cdrom, &opts);