This　paper　considers　covert　communications　in　the　context　of　unmanned　aerial　vehicle　(UAV)　networks,　aiming　to　hide　a　UAV　for　transmitting　critical　information　out　of　an　area　that　is　monitored　and　where　communication　is　not　allowed.　Specifically,　the　UAV　as　a　transmitter　intends　to　transmit　information　to　a　legitimate　receiver　(Bob)　covertly　while　avoiding　being　detected　by　a　warden　(Willie),　where　location　uncertainty　exists　at　Bob　and/or　Willie.　In　order　to　enhance　the　considered　covert　communication　performance,　we　jointly　optimize　the　UAV＇s　trajectory　and　transmit　power　in　terms　of　maximizing　the　average　covert　transmission　rate　from　the　UAV　to　Bob　subject　to　transmission　outage　constraint　and　covertness　constraint.　The　formulated　optimization　problem　is　difficult　to　tackle　directly　due　to　the　intractable　constraints.　As　such,　we　first　employ　conservative　approximation　to　transform　a　constraint　into　a　deterministic　form　and　then　apply　the　first-order　restrictive　approximation　to　transform　the　optimization　problem　into　a　convex　form.　By　applying　the　successive　convex　approximation　technique,　an　efficient　iterative　algorithm　is　developed　to　solve　the　optimization　problem.　Our　examination　shows　that　the　developed　joint　trajectory　and　transmit　power　optimization　scheme　achieves　significantly　better　covert　communication　performance　as　compared　to　a　benchmark　scheme.　©　1991-2012　IEEE.