diff --git a/mlir/include/mlir/Dialect/Complex/IR/ComplexOps.td b/mlir/include/mlir/Dialect/Complex/IR/ComplexOps.td
--- a/mlir/include/mlir/Dialect/Complex/IR/ComplexOps.td
+++ b/mlir/include/mlir/Dialect/Complex/IR/ComplexOps.td
@@ -564,4 +564,24 @@
   let results = (outs Complex<AnyFloat>:$result);
 }
 
+//===----------------------------------------------------------------------===//
+// Conj
+//===----------------------------------------------------------------------===//
+
+def ConjOp : ComplexUnaryOp<"conj", [SameOperandsAndResultType]> {
+  let summary = "Calculate the complex conjugate";
+  let description = [{
+    The `conj` op takes a single complex number and computes the
+    complex conjugate.
+
+    Example:
+
+    ```mlir
+    %a = complex.conj %b: complex<f32>
+    ```
+  }];
+
+  let results = (outs Complex<AnyFloat>:$result);
+}
+
 #endif // COMPLEX_OPS
diff --git a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
--- a/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
+++ b/mlir/lib/Conversion/ComplexToStandard/ComplexToStandard.cpp
@@ -885,6 +885,27 @@
   }
 };
 
+struct ConjOpConversion : public OpConversionPattern<complex::ConjOp> {
+  using OpConversionPattern<complex::ConjOp>::OpConversionPattern;
+
+  LogicalResult
+  matchAndRewrite(complex::ConjOp op, OpAdaptor adaptor,
+                  ConversionPatternRewriter &rewriter) const override {
+    auto loc = op.getLoc();
+    auto type = adaptor.getComplex().getType().cast<ComplexType>();
+    auto elementType = type.getElementType().cast<FloatType>();
+    Value real =
+        rewriter.create<complex::ReOp>(loc, elementType, adaptor.getComplex());
+    Value imag =
+        rewriter.create<complex::ImOp>(loc, elementType, adaptor.getComplex());
+    Value negImag = rewriter.create<arith::NegFOp>(loc, elementType, imag);
+
+    rewriter.replaceOpWithNewOp<complex::CreateOp>(op, type, real, negImag);
+
+    return success();
+  }
+};
+
 } // namespace
 
 void mlir::populateComplexToStandardConversionPatterns(
@@ -909,7 +930,8 @@
       SinOpConversion,
       SqrtOpConversion,
       TanOpConversion,
-      TanhOpConversion>(patterns.getContext());
+      TanhOpConversion,
+      ConjOpConversion>(patterns.getContext());
   // clang-format on
 }
 
diff --git a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
--- a/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
+++ b/mlir/test/Conversion/ComplexToStandard/convert-to-standard.mlir
@@ -663,3 +663,17 @@
   %sqrt = complex.sqrt %arg : complex<f32>
   return %sqrt : complex<f32>
 }
+
+// -----
+
+// CHECK-LABEL: func @complex_conj
+// CHECK-SAME: %[[ARG:.*]]: complex<f32>
+func.func @complex_conj(%arg: complex<f32>) -> complex<f32> {
+  %conj = complex.conj %arg: complex<f32>
+  return %conj : complex<f32>
+}
+// CHECK: %[[REAL:.*]] = complex.re %[[ARG]] : complex<f32>
+// CHECK: %[[IMAG:.*]] = complex.im %[[ARG]] : complex<f32>
+// CHECK: %[[NEG_IMAG:.*]] = arith.negf %[[IMAG]] : f32
+// CHECK: %[[RESULT:.*]] = complex.create %[[REAL]], %[[NEG_IMAG]] : complex<f32>
+// CHECK: return %[[RESULT]] : complex<f32>
\ No newline at end of file