In　this　paper,　we　present　a　complex-valued　projection　neural　network　for　solving　constrained　convex　optimization　problems　of　real　functions　with　complex　variables,　as　an　extension　of　real-valued　projection　neural　networks.　Theoretically,　by　developing　results　on　complex-valued　optimization　techniques,　we　prove　that　the　complex-valued　projection　neural　network　is　globally　stable　and　convergent　to　the　optimal　solution.　Obtained　results　are　completely　established　in　the　complex　domain　and　thus　significantly　generalize　existing　results　of　the　real-valued　projection　neural　networks.　Numerical　simulations　are　presented　to　confirm　the　obtained　results　and　effectiveness　of　the　proposed　complex-valued　projection　neural　network.