This　letter　considers　covert　communications　in　the　context　of　unmanned　aerial　vehicle　(UAV)　networks,　where　a　UAV　is　employed　as　a　base　station　to　transmit　covert　data　to　a　legitimate　ground　user,　while　ensuring　that　the　data　transmission　cannot　be　detected　by　a　warden.　Aiming　at　maximizing　the　legitimate　user＇s　average　effective　covert　throughput　(AECT),　the　UAV＇s　trajectory　and　transmit　power　are　jointly　optimized.　Taking　advantage　of　deep　reinforcement　learning　(DRL)　on　solving　dynamic　and　unpredictable　problems,　we　develop　a　twin-delayed　deep　deterministic　policy　gradient　aided　covert　transmission　algorithm　(TD3-CT),　to　determine　the　UAV＇s　optimal　trajectory　and　transmit　power.　Furthermore,　by　introducing　a　reward　shaping　mechanism,　the　convergence　of　the　algorithm　is　guaranteed.　The　experiment　results　show　that　the　developed　TD3-CT　algorithm　not　only　enables　the　covert　transmission　but　also　significantly　improves　its　performance　in　termed　of　achieving　a　higher　AECT,　compared　with　the　benchmark　schemes.