diff --git a/mlir/include/mlir/Dialect/Math/IR/MathOps.td b/mlir/include/mlir/Dialect/Math/IR/MathOps.td
--- a/mlir/include/mlir/Dialect/Math/IR/MathOps.td
+++ b/mlir/include/mlir/Dialect/Math/IR/MathOps.td
@@ -799,6 +799,7 @@
     %a = math.round %b : f64
     ```
   }];
+  let hasFolder = 1;
 }
 
 //===----------------------------------------------------------------------===//
diff --git a/mlir/lib/Dialect/Math/IR/MathOps.cpp b/mlir/lib/Dialect/Math/IR/MathOps.cpp
--- a/mlir/lib/Dialect/Math/IR/MathOps.cpp
+++ b/mlir/lib/Dialect/Math/IR/MathOps.cpp
@@ -427,6 +427,24 @@
   });
 }
 
+//===----------------------------------------------------------------------===//
+// RoundOp folder
+//===----------------------------------------------------------------------===//
+
+OpFoldResult math::RoundOp::fold(ArrayRef<Attribute> operands) {
+  return constFoldUnaryOpConditional<FloatAttr>(
+      operands, [](const APFloat &a) -> Optional<APFloat> {
+        switch (a.getSizeInBits(a.getSemantics())) {
+        case 64:
+          return APFloat(round(a.convertToDouble()));
+        case 32:
+          return APFloat(roundf(a.convertToFloat()));
+        default:
+          return {};
+        }
+      });
+}
+
 /// Materialize an integer or floating point constant.
 Operation *math::MathDialect::materializeConstant(OpBuilder &builder,
                                                   Attribute value, Type type,
diff --git a/mlir/test/Dialect/Math/canonicalize.mlir b/mlir/test/Dialect/Math/canonicalize.mlir
--- a/mlir/test/Dialect/Math/canonicalize.mlir
+++ b/mlir/test/Dialect/Math/canonicalize.mlir
@@ -393,3 +393,21 @@
   %0 = math.roundeven %v1 : vector<4xf32>
   return %0 : vector<4xf32>
 }
+
+// CHECK-LABEL: @round_fold
+// CHECK-NEXT: %[[cst:.+]] = arith.constant 2.000000e+00 : f32
+// CHECK-NEXT:   return %[[cst]]
+func.func @round_fold() -> f32 {
+  %c = arith.constant 1.5 : f32
+  %r = math.round %c : f32
+  return %r : f32
+}
+
+// CHECK-LABEL: @round_fold_vec
+// CHECK-NEXT: %[[cst:.+]] = arith.constant dense<[1.000000e+00, -1.000000e+00, 2.000000e+00, -2.000000e+00]> : vector<4xf32>
+// CHECK-NEXT:   return %[[cst]]
+func.func @round_fold_vec() -> (vector<4xf32>) {
+  %v1 = arith.constant dense<[0.5, -0.5, 1.5, -1.5]> : vector<4xf32>
+  %0 = math.round %v1 : vector<4xf32>
+  return %0 : vector<4xf32>
+}