diff --git a/fs/operations/operations.go b/fs/operations/operations.go
index 820737841..a142140a2 100644
--- a/fs/operations/operations.go
+++ b/fs/operations/operations.go
@@ -19,6 +19,7 @@ import (
 
 	"github.com/ncw/rclone/fs"
 	"github.com/ncw/rclone/fs/accounting"
+	"github.com/ncw/rclone/fs/cache"
 	"github.com/ncw/rclone/fs/fserrors"
 	"github.com/ncw/rclone/fs/fshttp"
 	"github.com/ncw/rclone/fs/hash"
@@ -1475,6 +1476,22 @@ func moveOrCopyFile(fdst fs.Fs, fsrc fs.Fs, dstFileName string, srcFileName stri
 	}
 
 	if NeedTransfer(dstObj, srcObj) {
+		// If destination already exists, then we must move it into --backup-dir if required
+		if dstObj != nil && fs.Config.BackupDir != "" {
+			backupDir, err := cache.Get(fs.Config.BackupDir)
+			if err != nil {
+				return errors.Wrap(err, "creating Fs for --backup-dir failed")
+			}
+			remoteWithSuffix := SuffixName(dstObj.Remote())
+			overwritten, _ := backupDir.NewObject(remoteWithSuffix)
+			_, err = Move(backupDir, overwritten, remoteWithSuffix, dstObj)
+			if err != nil {
+				return errors.Wrap(err, "moving to --backup-dir failed")
+			}
+			// If successful zero out the dstObj as it is no longer there
+			dstObj = nil
+		}
+
 		_, err = Op(fdst, dstObj, dstFileName, srcObj)
 	} else {
 		accounting.Stats.Checking(srcFileName)
diff --git a/fs/operations/operations_test.go b/fs/operations/operations_test.go
index 42cbd8945..09cc60c64 100644
--- a/fs/operations/operations_test.go
+++ b/fs/operations/operations_test.go
@@ -739,6 +739,29 @@ func TestMoveFile(t *testing.T) {
 	fstest.CheckItems(t, r.Fremote, file2)
 }
 
+func TestMoveFileBackupDir(t *testing.T) {
+	r := fstest.NewRun(t)
+	defer r.Finalise()
+
+	oldBackupDir := fs.Config.BackupDir
+	fs.Config.BackupDir = r.FremoteName + "/backup"
+	defer func() {
+		fs.Config.BackupDir = oldBackupDir
+	}()
+
+	file1 := r.WriteFile("dst/file1", "file1 contents", t1)
+	fstest.CheckItems(t, r.Flocal, file1)
+
+	file1old := r.WriteObject("dst/file1", "file1 contents old", t1)
+	fstest.CheckItems(t, r.Fremote, file1old)
+
+	err := operations.MoveFile(r.Fremote, r.Flocal, file1.Path, file1.Path)
+	require.NoError(t, err)
+	fstest.CheckItems(t, r.Flocal)
+	file1old.Path = "backup/dst/file1"
+	fstest.CheckItems(t, r.Fremote, file1old, file1)
+}
+
 func TestCopyFile(t *testing.T) {
 	r := fstest.NewRun(t)
 	defer r.Finalise()
@@ -765,6 +788,29 @@ func TestCopyFile(t *testing.T) {
 	fstest.CheckItems(t, r.Fremote, file2)
 }
 
+func TestCopyFileBackupDir(t *testing.T) {
+	r := fstest.NewRun(t)
+	defer r.Finalise()
+
+	oldBackupDir := fs.Config.BackupDir
+	fs.Config.BackupDir = r.FremoteName + "/backup"
+	defer func() {
+		fs.Config.BackupDir = oldBackupDir
+	}()
+
+	file1 := r.WriteFile("dst/file1", "file1 contents", t1)
+	fstest.CheckItems(t, r.Flocal, file1)
+
+	file1old := r.WriteObject("dst/file1", "file1 contents old", t1)
+	fstest.CheckItems(t, r.Fremote, file1old)
+
+	err := operations.CopyFile(r.Fremote, r.Flocal, file1.Path, file1.Path)
+	require.NoError(t, err)
+	fstest.CheckItems(t, r.Flocal, file1)
+	file1old.Path = "backup/dst/file1"
+	fstest.CheckItems(t, r.Fremote, file1old, file1)
+}
+
 // testFsInfo is for unit testing fs.Info
 type testFsInfo struct {
 	name      string