diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -2787,6 +2787,14 @@
     break;
   case Instruction::Add: {
     // X + Y.
+
+    // If Add has nuw wrap flag, then if either X or Y is non-zero the result is
+    // non-zero.
+    auto *BO = cast<OverflowingBinaryOperator>(V);
+    if (Q.IIQ.hasNoUnsignedWrap(BO))
+      return isKnownNonZero(I->getOperand(0), DemandedElts, Depth, Q) ||
+             isKnownNonZero(I->getOperand(1), DemandedElts, Depth, Q);
+
     KnownBits XKnown =
         computeKnownBits(I->getOperand(0), DemandedElts, Depth, Q);
     KnownBits YKnown =
diff --git a/llvm/test/Analysis/ValueTracking/known-non-zero.ll b/llvm/test/Analysis/ValueTracking/known-non-zero.ll
--- a/llvm/test/Analysis/ValueTracking/known-non-zero.ll
+++ b/llvm/test/Analysis/ValueTracking/known-non-zero.ll
@@ -473,9 +473,7 @@
 ; CHECK-LABEL: @add_nonzero_nuw(
 ; CHECK-NEXT:    [[X_NZ:%.*]] = icmp ne i8 [[X:%.*]], 0
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[X_NZ]])
-; CHECK-NEXT:    [[A:%.*]] = add nuw i8 [[X]], [[Y:%.*]]
-; CHECK-NEXT:    [[R:%.*]] = icmp eq i8 [[A]], 0
-; CHECK-NEXT:    ret i1 [[R]]
+; CHECK-NEXT:    ret i1 false
 ;
   %x_nz = icmp ne i8 %x, 0
   call void @llvm.assume(i1 %x_nz)