diff --git a/llvm/lib/Transforms/Scalar/MemCpyOptimizer.cpp b/llvm/lib/Transforms/Scalar/MemCpyOptimizer.cpp
index b9efd9aaa28c5..9bf87f2370531 100644
--- a/llvm/lib/Transforms/Scalar/MemCpyOptimizer.cpp
+++ b/llvm/lib/Transforms/Scalar/MemCpyOptimizer.cpp
@@ -1161,6 +1161,14 @@ bool MemCpyOptPass::processMemCpyMemCpyDependence(MemCpyInst *M,
                      MSSA->getMemoryAccess(MDep), MSSA->getMemoryAccess(M)))
     return false;
 
+  // No need to create `memcpy(a <- a)`.
+  if (BAA.isMustAlias(M->getDest(), MDep->getSource())) {
+    // Remove the instruction we're replacing.
+    eraseInstruction(M);
+    ++NumMemCpyInstr;
+    return true;
+  }
+
   // If the dest of the second might alias the source of the first, then the
   // source and dest might overlap. In addition, if the source of the first
   // points to constant memory, they won't overlap by definition. Otherwise, we
diff --git a/llvm/test/Transforms/MemCpyOpt/memcpy.ll b/llvm/test/Transforms/MemCpyOpt/memcpy.ll
index 48698f25174e7..1d55c733da831 100644
--- a/llvm/test/Transforms/MemCpyOpt/memcpy.ll
+++ b/llvm/test/Transforms/MemCpyOpt/memcpy.ll
@@ -139,6 +139,37 @@ define void @test6_memcpy(ptr %src, ptr %dest) nounwind {
   ret void
 }
 
+; When forwarding to memcpy(arg+1, arg+1), we don't need to create this memcpy.
+define void @test6_memcpy_forward_back(ptr %arg) nounwind {
+; CHECK-LABEL: @test6_memcpy_forward_back(
+; CHECK-NEXT:    [[DEST:%.*]] = getelementptr inbounds i8, ptr [[ARG:%.*]], i64 1
+; CHECK-NEXT:    ret void
+;
+  %tmp = alloca [16 x i8], align 1
+  %src = getelementptr inbounds i8, ptr %arg, i64 1
+  %dest = getelementptr inbounds i8, ptr %arg, i64 1
+  call void @llvm.memcpy.inline.p0.p0.i32(ptr align 1 %tmp, ptr align 1 %src, i32 16, i1 false)
+  call void @llvm.memcpy.inline.p0.p0.i32(ptr align 1 %dest, ptr align 1 %tmp, i32 16, i1 false)
+  ret void
+}
+
+; We have to retain this `memcpy(arg+2, arg+1)` forwarding.
+define void @test6_memcpy_forward_not_back(ptr %arg) nounwind {
+; CHECK-LABEL: @test6_memcpy_forward_not_back(
+; CHECK-NEXT:    [[TMP:%.*]] = alloca [16 x i8], align 1
+; CHECK-NEXT:    [[SRC:%.*]] = getelementptr inbounds i8, ptr [[ARG:%.*]], i64 1
+; CHECK-NEXT:    [[DEST:%.*]] = getelementptr inbounds i8, ptr [[ARG]], i64 2
+; CHECK-NEXT:    call void @llvm.memcpy.inline.p0.p0.i32(ptr align 1 [[TMP]], ptr align 1 [[SRC]], i32 16, i1 false)
+; CHECK-NEXT:    call void @llvm.memcpy.inline.p0.p0.i32(ptr align 1 [[DEST]], ptr align 1 [[TMP]], i32 16, i1 false)
+; CHECK-NEXT:    ret void
+;
+  %tmp = alloca [16 x i8], align 1
+  %src = getelementptr inbounds i8, ptr %arg, i64 1
+  %dest = getelementptr inbounds i8, ptr %arg, i64 2
+  call void @llvm.memcpy.inline.p0.p0.i32(ptr align 1 %tmp, ptr align 1 %src, i32 16, i1 false)
+  call void @llvm.memcpy.inline.p0.p0.i32(ptr align 1 %dest, ptr align 1 %tmp, i32 16, i1 false)
+  ret void
+}
 
 @x = external global %0