diff --git a/src/uu/cp/src/cp.rs b/src/uu/cp/src/cp.rs
index f8ce6f241..fa9a1df65 100644
--- a/src/uu/cp/src/cp.rs
+++ b/src/uu/cp/src/cp.rs
@@ -1309,6 +1309,15 @@ fn copy_file(
 
     match options.copy_mode {
         CopyMode::Link => {
+            if dest.exists() {
+                let backup_path =
+                    backup_control::get_backup_path(options.backup, &dest, &options.backup_suffix);
+                if let Some(backup_path) = backup_path {
+                    backup_dest(&dest, &backup_path)?;
+                    fs::remove_file(&dest)?;
+                }
+            }
+
             fs::hard_link(&source, &dest).context(context)?;
         }
         CopyMode::Copy => {
diff --git a/tests/by-util/test_cp.rs b/tests/by-util/test_cp.rs
index 92637dfbe..52081eb52 100644
--- a/tests/by-util/test_cp.rs
+++ b/tests/by-util/test_cp.rs
@@ -1444,3 +1444,17 @@ fn test_cp_archive_on_nonexistent_file() {
             "cp: cannot stat 'nonexistent_file.txt': No such file or directory (os error 2)",
         );
 }
+
+#[test]
+fn test_cp_link_backup() {
+    let (at, mut ucmd) = at_and_ucmd!();
+    at.touch("file2");
+    ucmd.arg("-l")
+        .arg("-b")
+        .arg(TEST_HELLO_WORLD_SOURCE)
+        .arg("file2")
+        .succeeds();
+
+    assert!(at.file_exists("file2~"));
+    assert_eq!(at.read("file2"), "Hello, World!\n");
+}