diff --git a/include/mlir-hlo/Dialect/mhlo/transforms/map_lmhlo_to_scalar_op.h b/include/mlir-hlo/Dialect/mhlo/transforms/map_lmhlo_to_scalar_op.h
index 91ed8f0..7b18b4f 100644
--- a/include/mlir-hlo/Dialect/mhlo/transforms/map_lmhlo_to_scalar_op.h
+++ b/include/mlir-hlo/Dialect/mhlo/transforms/map_lmhlo_to_scalar_op.h
@@ -279,6 +279,16 @@ inline Value MapCompareOpToStdScalarOp(Location loc,
     return b->create<ScalarFOp<CompareOpTy>>(loc, predicate.getValue(), lhs,
                                              rhs);
   }
+  if (auto complex_type = element_type.dyn_cast<ComplexType>()) {
+    if (complex_type.getElementType().isa<FloatType>()) {
+      if (comparison_direction == "EQ") {
+        return b->create<complex::EqualOp>(loc, lhs, rhs);
+      }
+      if (comparison_direction == "NE") {
+        return b->create<complex::NotEqualOp>(loc, lhs, rhs);
+      }
+    }
+  }
   return nullptr;
 }
 
diff --git a/tests/lhlo-legalize-to-linalg.mlir b/tests/lhlo-legalize-to-linalg.mlir
index 079838f..ab3dfea 100644
--- a/tests/lhlo-legalize-to-linalg.mlir
+++ b/tests/lhlo-legalize-to-linalg.mlir
@@ -188,7 +188,7 @@ func @float_cmp(%lhs: memref<2x2xf32>, %rhs: memref<2x2xf32>,
 
 // CHECK-LABEL: func @int_cmp
 func @int_cmp(%lhs: memref<2x2xi32>, %rhs: memref<2x2xi32>,
-          %result: memref<2x2xi1>) {
+              %result: memref<2x2xi1>) {
   "lmhlo.compare"(%lhs, %rhs, %result) {comparison_direction = "LT"}
       : (memref<2x2xi32>, memref<2x2xi32>, memref<2x2xi1>) -> ()
   return
@@ -200,6 +200,34 @@ func @int_cmp(%lhs: memref<2x2xi32>, %rhs: memref<2x2xi32>,
 
 // -----
 
+// CHECK-LABEL: func @complex_cmp_eq
+func @complex_cmp_eq(%lhs: memref<2xcomplex<f32>>, %rhs: memref<2xcomplex<f32>>,
+                     %result: memref<2xi1>) {
+  "lmhlo.compare"(%lhs, %rhs, %result) {comparison_direction = "EQ"}
+      : (memref<2xcomplex<f32>>, memref<2xcomplex<f32>>, memref<2xi1>) -> ()
+  return
+}
+// CHECK: linalg.generic
+// CHECK-NEXT: ^bb0(%[[LHS_IN:.*]]: complex<f32>, %[[RHS_IN:.*]]: complex<f32>, %[[RESULT_OUT:.*]]: i1):
+// CHECK-NEXT:   %[[RESULT:.*]] = complex.eq %[[LHS_IN]], %[[RHS_IN]] : complex<f32>
+// CHECK-NEXT:   linalg.yield %[[RESULT]] : i1
+
+// -----
+
+// CHECK-LABEL: func @complex_cmp_neq
+func @complex_cmp_neq(%lhs: memref<2xcomplex<f64>>, %rhs: memref<2xcomplex<f64>>,
+                      %result: memref<2xi1>) {
+  "lmhlo.compare"(%lhs, %rhs, %result) {comparison_direction = "NE"}
+      : (memref<2xcomplex<f64>>, memref<2xcomplex<f64>>, memref<2xi1>) -> ()
+  return
+}
+// CHECK: linalg.generic
+// CHECK-NEXT: ^bb0(%[[LHS_IN:.*]]: complex<f64>, %[[RHS_IN:.*]]: complex<f64>, %[[RESULT_OUT:.*]]: i1):
+// CHECK-NEXT:   %[[RESULT:.*]] = complex.neq %[[LHS_IN]], %[[RHS_IN]] : complex<f64>
+// CHECK-NEXT:   linalg.yield %[[RESULT]] : i1
+
+// -----
+
 // CHECK-LABEL: func @select
 func @select(%pred: memref<2x2xi1>, %lhs: memref<2x2xf32>,
              %rhs: memref<2x2xf32>, %result: memref<2x2xf32>) {