This　paper　considers　covert　communications　in　the　context　of　unmanned　aerial　vehicle　(UAV)　networks　where　the　UAV　is　employed　as　a　transmitter　to　covertly　disseminate　data　to　a　group　of　legitimate　receivers　on　the　ground,　while　ensuring　that　the　data　dissemination　is　not　detected　by　the　wardens.　Considering　the　endurance　time　limit　of　UAV,　our　goal　is　to　minimize　the　UAV＇s　mission　completion　time　by　jointly　optimizing　the　trajectory　of　UAV　and　the　ground　receivers＇　schedule.　Since　the　environment　considered　is　dynamic,　the　optimization　problem　is　firstly　modeled　as　a　Markov　decision　process.　Taking　the　advantage　of　the　deep　reinforcement　learning　(DRL)　to　learn　dynamically　from　the　environment,　we　propose　a　twin-delayed　deep　deterministic　policy　gradient　(TD3)　aided　covert　data　dissemination　(TD3-CDD)　algorithm.　In　particular,　we　developed　an　advanced　reward　design　mechanism　to　ensure　the　effectiveness　of　the　constraints　on　UAV.　Our　examination　shows　that　the　TD3-CDD　algorithm　enables　the　UAV　to　complete　covert　data　dissemination　in　a　shorter　time　than　a　benchmark　scheme.　©　2022　IEEE.