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
@@ -541,6 +541,7 @@
     %y = math.log1p %x : 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
@@ -128,6 +128,28 @@
       });
 }
 
+//===----------------------------------------------------------------------===//
+// Log1pOp folder
+//===----------------------------------------------------------------------===//
+
+OpFoldResult math::Log1pOp::fold(ArrayRef<Attribute> operands) {
+  return constFoldUnaryOpConditional<FloatAttr>(
+      operands, [](const APFloat &a) -> Optional<APFloat> {
+        switch (a.getSizeInBits(a.getSemantics())) {
+        case 64:
+          if ((a + APFloat(1.0)).isNegative())
+            return {};
+          return APFloat(log1p(a.convertToDouble()));
+        case 32:
+          if ((a + APFloat(1.0f)).isNegative())
+            return {};
+          return APFloat(log1pf(a.convertToFloat()));
+        default:
+          return {};
+        }
+      });
+}
+
 //===----------------------------------------------------------------------===//
 // PowFOp folder
 //===----------------------------------------------------------------------===//
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
@@ -192,3 +192,21 @@
   %0 = math.log10 %v1 : vector<4xf32>
   return %0 : vector<4xf32>
 }
+
+// CHECK-LABEL: @log1p_fold
+// CHECK: %[[cst:.+]] = arith.constant 2.8903718 : f32
+  // CHECK: return %[[cst]]
+func.func @log1p_fold() -> f32 {
+  %c = arith.constant 17.0 : f32
+  %r = math.log1p %c : f32
+  return %r : f32
+}
+
+// CHECK-LABEL: @log1p_fold_vec
+// CHECK: %[[cst:.+]] = arith.constant dense<[1.38629436, 1.79175949, 2.07944155, 2.48490667]> : vector<4xf32>
+// CHECK: return %[[cst]]
+func.func @log1p_fold_vec() -> (vector<4xf32>) {
+  %v1 = arith.constant dense<[3.0, 5.0, 7.0, 11.0]> : vector<4xf32>
+  %0 = math.log1p %v1 : vector<4xf32>
+  return %0 : vector<4xf32>
+}