As　a　promising　technique　for　offloading　computation　tasks　from　mobile　devices,　Unmanned　Aerial　Vehicle　(UAV)-　assisted　Mobile　Edge　Computing　(MEC)　utilizes　UAVs　as　computational　resources.　A　popular　method　for　enhancing　the　quality　of　service　(QoS)　of　UAV-assisted　MEC　systems　is　to　jointly　optimize　UAV　deployment　and　computation　task　offloading.　This　imposes　the　challenge　of　dynamically　adjusting　UAV　deployment　and　computation　offloading　to　accommodate　the　changing　positions　and　computational　requirements　of　mobile　devices.　Due　to　the　real-time　requirements　of　MEC　computation　tasks,　finding　an　efficient　joint　optimization　approach　is　imperative.　This　paper　proposes　an　algorithm　aimed　at　minimizing　the　average　response　delay　in　a　UAV-assisted　MEC　system.　The　approach　revolves　around　the　joint　optimization　of　UAV　deployment　and　computation　offloading　through　convex　optimization.　We　break　down　the　problem　into　three　sub-problems:　UAV　deployment,　Ground　Device　(GD)　access,　and　computation　tasks　offloading,　which　we　address　using　the　block　coordinate　descent　algorithm.　Observing　the　NP-hardness　nature　of　the　original　problem,　we　present　near-optimal　solutions　to　the　decomposed　sub-problems.　Simulation　results　demonstrate　that　our　approach　can　generate　a　joint　optimization　solution　within　seconds　and　diminish　the　average　response　delay　compared　to　state-of-the-art　algorithms　and　other　advanced　algorithms,　with　improvements　ranging　from　4.70%　to　42.94%.　　©　2013　IEEE.