In　this　letter,　we　consider　delay-constrained　covert　communications　with　the　aid　of　a　full-duplex　(FD)　receiver.　Without　delay　constraints,　it　has　been　shown　that　the　transmit　power　of　artificial　noise　(AN)　at　the　FD　receiver　should　be　random　in　order　to　enhance　covert　communications.　In　this　letter,　we　show　that　transmitting　AN　with　a　fixed　power　indeed　improve　covert　communications　with　delay　constraints,　since　in　a　limited　time　period　the　warden　cannot　exactly　learn　its　received　power.　This　explicitly　shows　one　benefit　of　considering　practical　delay　constraints　in　the　context　of　covert　communications.　We　analyze　the　optimal　transmit　power　of　AN　for　either　fixed　or　globally　optimized　transmit　power　of　covert　information,　based　on　which　we　also　determine　the　specific　condition　under　which　transmitting　AN　by　the　FD　receiver　can　aid　covert　communications　and　a　larger　transmit　power　of　AN　always　leads　to　better　covert　communication　performance.