diff --git a/flang/lib/Optimizer/CodeGen/CodeGen.cpp b/flang/lib/Optimizer/CodeGen/CodeGen.cpp
--- a/flang/lib/Optimizer/CodeGen/CodeGen.cpp
+++ b/flang/lib/Optimizer/CodeGen/CodeGen.cpp
@@ -586,6 +586,38 @@
   }
 };
 
+/// Lower complex constants
+struct ConstcOpConversion : public FIROpConversion<fir::ConstcOp> {
+  using FIROpConversion::FIROpConversion;
+
+  mlir::LogicalResult
+  matchAndRewrite(fir::ConstcOp conc, OpAdaptor,
+                  mlir::ConversionPatternRewriter &rewriter) const override {
+    mlir::Location loc = conc.getLoc();
+    mlir::MLIRContext *ctx = conc.getContext();
+    mlir::Type ty = convertType(conc.getType());
+    mlir::Type ety = convertType(getComplexEleTy(conc.getType()));
+    auto realFloatAttr = mlir::FloatAttr::get(ety, getValue(conc.getReal()));
+    auto realPart =
+        rewriter.create<mlir::LLVM::ConstantOp>(loc, ety, realFloatAttr);
+    auto imFloatAttr = mlir::FloatAttr::get(ety, getValue(conc.getImaginary()));
+    auto imPart =
+        rewriter.create<mlir::LLVM::ConstantOp>(loc, ety, imFloatAttr);
+    auto realIndex = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(0));
+    auto imIndex = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(1));
+    auto undef = rewriter.create<mlir::LLVM::UndefOp>(loc, ty);
+    auto setReal = rewriter.create<mlir::LLVM::InsertValueOp>(
+        loc, ty, undef, realPart, realIndex);
+    rewriter.replaceOpWithNewOp<mlir::LLVM::InsertValueOp>(conc, ty, setReal,
+                                                           imPart, imIndex);
+    return success();
+  }
+
+  inline APFloat getValue(mlir::Attribute attr) const {
+    return attr.cast<fir::RealAttr>().getValue();
+  }
+};
+
 /// convert value of from-type to value of to-type
 struct ConvertOpConversion : public FIROpConversion<fir::ConvertOp> {
   using FIROpConversion::FIROpConversion;
@@ -1685,17 +1717,18 @@
         BoxDimsOpConversion, BoxEleSizeOpConversion, BoxIsAllocOpConversion,
         BoxIsArrayOpConversion, BoxIsPtrOpConversion, BoxRankOpConversion,
         BoxTypeDescOpConversion, CallOpConversion, CmpcOpConversion,
-        ConvertOpConversion, DispatchOpConversion, DispatchTableOpConversion,
-        DTEntryOpConversion, DivcOpConversion, EmboxCharOpConversion,
-        ExtractValueOpConversion, HasValueOpConversion, GenTypeDescOpConversion,
-        GlobalLenOpConversion, GlobalOpConversion, InsertOnRangeOpConversion,
-        InsertValueOpConversion, IsPresentOpConversion, LoadOpConversion,
-        NegcOpConversion, MulcOpConversion, SelectCaseOpConversion,
-        SelectOpConversion, SelectRankOpConversion, SelectTypeOpConversion,
-        ShapeOpConversion, ShapeShiftOpConversion, ShiftOpConversion,
-        SliceOpConversion, StoreOpConversion, StringLitOpConversion,
-        SubcOpConversion, UnboxCharOpConversion, UndefOpConversion,
-        UnreachableOpConversion, ZeroOpConversion>(typeConverter);
+        ConstcOpConversion, ConvertOpConversion, DispatchOpConversion,
+        DispatchTableOpConversion, DTEntryOpConversion, DivcOpConversion,
+        EmboxCharOpConversion, ExtractValueOpConversion, HasValueOpConversion,
+        GenTypeDescOpConversion, GlobalLenOpConversion, GlobalOpConversion,
+        InsertOnRangeOpConversion, InsertValueOpConversion,
+        IsPresentOpConversion, LoadOpConversion, NegcOpConversion,
+        MulcOpConversion, SelectCaseOpConversion, SelectOpConversion,
+        SelectRankOpConversion, SelectTypeOpConversion, ShapeOpConversion,
+        ShapeShiftOpConversion, ShiftOpConversion, SliceOpConversion,
+        StoreOpConversion, StringLitOpConversion, SubcOpConversion,
+        UnboxCharOpConversion, UndefOpConversion, UnreachableOpConversion,
+        ZeroOpConversion>(typeConverter);
     mlir::populateStdToLLVMConversionPatterns(typeConverter, pattern);
     mlir::arith::populateArithmeticToLLVMConversionPatterns(typeConverter,
                                                             pattern);
diff --git a/flang/test/Fir/convert-to-llvm.fir b/flang/test/Fir/convert-to-llvm.fir
--- a/flang/test/Fir/convert-to-llvm.fir
+++ b/flang/test/Fir/convert-to-llvm.fir
@@ -690,6 +690,38 @@
 
 // -----
 
+// Test constc.
+
+func @test_constc4() -> !fir.complex<4> {
+  %0 = fir.constc (#fir.real<4, 1.4>, #fir.real<4, 2.3>) : !fir.complex<4>
+  return %0 : !fir.complex<4>
+}
+
+// CHECK-LABEL: @test_constc4
+// CHECK_SAME: () -> !llvm.struct<(f32, f32)>
+// CHECK-DAG: [[rp:%.*]] = llvm.mlir.constant(1.400000e+00 : f32) : f32
+// CHECK-DAG: [[ip:%.*]] = llvm.mlir.constant(2.300000e+00 : f32) : f32
+// CHECK: [[undef:%.*]] = llvm.mlir.undef : !llvm.struct<(f32, f32)>
+// CHECK: [[withr:%.*]] = llvm.insertvalue [[rp]], [[undef]][0 : i32] : !llvm.struct<(f32, f32)>
+// CHECK: [[full:%.*]] = llvm.insertvalue [[ip]], [[withr]][1 : i32] : !llvm.struct<(f32, f32)>
+// CHECK: return [[full]] : !llvm.struct<(f32, f32)>
+
+func @test_constc8() -> !fir.complex<8> {
+  %0 = fir.constc (#fir.real<8, 1.8>, #fir.real<8, 2.3>) : !fir.complex<8>
+  return %0 : !fir.complex<8>
+}
+
+// CHECK-LABEL: @test_constc8
+// CHECK_SAME: () -> !llvm.struct<(f64, f64)>
+// CHECK-DAG: [[rp:%.*]] = llvm.mlir.constant(1.800000e+00 : f64) : f64
+// CHECK-DAG: [[ip:%.*]] = llvm.mlir.constant(2.300000e+00 : f64) : f64
+// CHECK: [[undef:%.*]] = llvm.mlir.undef : !llvm.struct<(f64, f64)>
+// CHECK: [[withr:%.*]] = llvm.insertvalue [[rp]], [[undef]][0 : i32] : !llvm.struct<(f64, f64)>
+// CHECK: [[full:%.*]] = llvm.insertvalue [[ip]], [[withr]][1 : i32] : !llvm.struct<(f64, f64)>
+// CHECK: return [[full]] : !llvm.struct<(f64, f64)>
+
+// -----
+
 // Test `fir.store` --> `llvm.store` conversion
 
 func @test_store_index(%val_to_store : index, %addr : !fir.ref<index>) {