Index: flang/lib/Optimizer/CodeGen/CodeGen.cpp
===================================================================
--- flang/lib/Optimizer/CodeGen/CodeGen.cpp
+++ flang/lib/Optimizer/CodeGen/CodeGen.cpp
@@ -566,6 +566,34 @@
   }
 };
 
+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 ri = mlir::FloatAttr::get(ety, getValue(conc.getReal()));
+    auto rp = rewriter.create<mlir::LLVM::ConstantOp>(loc, ety, ri);
+    auto ii = mlir::FloatAttr::get(ety, getValue(conc.getImaginary()));
+    auto ip = rewriter.create<mlir::LLVM::ConstantOp>(loc, ety, ii);
+    auto c0 = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(0));
+    auto c1 = mlir::ArrayAttr::get(ctx, rewriter.getI32IntegerAttr(1));
+    auto r = rewriter.create<mlir::LLVM::UndefOp>(loc, ty);
+    auto rr = rewriter.create<mlir::LLVM::InsertValueOp>(loc, ty, r, rp, c0);
+    rewriter.replaceOpWithNewOp<mlir::LLVM::InsertValueOp>(conc, ty, rr, ip,
+                                                           c1);
+    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;
@@ -1628,17 +1656,17 @@
         AllocaOpConversion, BoxAddrOpConversion, BoxCharLenOpConversion,
         BoxDimsOpConversion, BoxEleSizeOpConversion, BoxIsAllocOpConversion,
         BoxIsArrayOpConversion, BoxIsPtrOpConversion, BoxRankOpConversion,
-        CallOpConversion, CmpcOpConversion, ConvertOpConversion,
-        DispatchOpConversion, DispatchTableOpConversion, DTEntryOpConversion,
-        DivcOpConversion, EmboxCharOpConversion, ExtractValueOpConversion,
-        HasValueOpConversion, GenTypeDescOpConversion, GlobalLenOpConversion,
-        GlobalOpConversion, InsertOnRangeOpConversion, InsertValueOpConversion,
-        IsPresentOpConversion, LoadOpConversion, NegcOpConversion,
-        MulcOpConversion, SelectCaseOpConversion, SelectOpConversion,
-        SelectRankOpConversion, SelectTypeOpConversion, StoreOpConversion,
-        StringLitOpConversion, SubcOpConversion, UnboxCharOpConversion,
-        UndefOpConversion, UnreachableOpConversion, ZeroOpConversion>(
-        typeConverter);
+        CallOpConversion, CmpcOpConversion, ConstcOpConversion,
+        ConvertOpConversion, DispatchOpConversion, DispatchTableOpConversion,
+        DTEntryOpConversion, DivcOpConversion, EmboxCharOpConversion,
+        ExtractValueOpConversion, HasValueOpConversion, GenTypeDescOpConversion,
+        GlobalLenOpConversion, GlobalOpConversion, InsertOnRangeOpConversion,
+        InsertValueOpConversion, IsPresentOpConversion, LoadOpConversion,
+        NegcOpConversion, MulcOpConversion, SelectCaseOpConversion,
+        SelectOpConversion, SelectRankOpConversion, SelectTypeOpConversion,
+        StoreOpConversion, StringLitOpConversion, SubcOpConversion,
+        UnboxCharOpConversion, UndefOpConversion, UnreachableOpConversion,
+        ZeroOpConversion>(typeConverter);
     mlir::populateStdToLLVMConversionPatterns(typeConverter, pattern);
     mlir::arith::populateArithmeticToLLVMConversionPatterns(typeConverter,
                                                             pattern);
Index: flang/test/Fir/convert-to-llvm.fir
===================================================================
--- flang/test/Fir/convert-to-llvm.fir
+++ flang/test/Fir/convert-to-llvm.fir
@@ -690,6 +690,24 @@
 
 // -----
 
+// Test constc.
+
+func @test_constc() -> !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_constc
+// 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)>
+
+// -----
+
 // Test `fir.store` --> `llvm.store` conversion
 
 func @test_store_index(%val_to_store : index, %addr : !fir.ref<index>) {