diff --git a/clippy_lints/src/escape.rs b/clippy_lints/src/escape.rs
index 2c6bfae6efe1..d15a619ef9f0 100644
--- a/clippy_lints/src/escape.rs
+++ b/clippy_lints/src/escape.rs
@@ -102,8 +102,8 @@ impl<'a, 'tcx> LateLintPass<'a, 'tcx> for Pass {
 impl<'a, 'tcx> Delegate<'tcx> for EscapeDelegate<'a, 'tcx> {
     fn consume(&mut self, _: HirId, _: Span, cmt: &cmt_<'tcx>, mode: ConsumeMode) {
         if let Categorization::Local(lid) = cmt.cat {
-            if let Move(DirectRefMove) = mode {
-                // Moved out or in. Clearly can't be localized.
+            if let Move(DirectRefMove) | Move(CaptureMove) = mode {
+                // moved out or in. clearly can't be localized
                 self.set.remove(&lid);
             }
         }
diff --git a/tests/ui/escape_analysis.rs b/tests/ui/escape_analysis.rs
index f582596eb56a..e3f78182fd13 100644
--- a/tests/ui/escape_analysis.rs
+++ b/tests/ui/escape_analysis.rs
@@ -148,3 +148,23 @@ trait MyTrait {
 impl<T> MyTrait for Box<T> {
     fn do_sth(self) {}
 }
+
+// Issue #3739 - capture in closures
+mod issue_3739 {
+    use super::A;
+
+    fn consume<T>(_: T) {}
+    fn borrow<T>(_: &T) {}
+
+    fn closure_consume(x: Box<A>) {
+        let _ = move || {
+            consume(x);
+        };
+    }
+
+    fn closure_borrow(x: Box<A>) {
+        let _ = || {
+            borrow(&x);
+        };
+    }
+}
diff --git a/tests/ui/escape_analysis.stderr b/tests/ui/escape_analysis.stderr
index 8af211f8a1a9..3944acd87f28 100644
--- a/tests/ui/escape_analysis.stderr
+++ b/tests/ui/escape_analysis.stderr
@@ -12,5 +12,11 @@ error: local variable doesn't need to be boxed here
 LL | pub fn new(_needs_name: Box<PeekableSeekable<&()>>) -> () {}
    |            ^^^^^^^^^^^
 
-error: aborting due to 2 previous errors
+error: local variable doesn't need to be boxed here
+  --> $DIR/escape_analysis.rs:165:23
+   |
+LL |     fn closure_borrow(x: Box<A>) {
+   |                       ^
+
+error: aborting due to 3 previous errors