With　the　expansion　of　cities　and　emerging　complicated　application,smart　city　has　become　an　intelligent　management　mechanism.　In　order　to　guarantee　the　information　security　and　quality　of　service　(QoS)　of　the　Internet　of　Thing(IoT)　devices　in　the　smart　city,a　mobile　edge　computing　(MEC)　enabled　blockchain　system　is　considered　as　the　smart　city　scenario　where　the　offloading　process　of　computing　tasks　is　a　key　aspect　infecting　the　system　performance　in　terms　of　service　profit　and　latency.　The　task　offloading　process　is　formulated　as　a　Markov　decision　process　(MDP)　and　the　optimal　goal　is　the　cumulative　profit　for　the　offloading　nodes　considering　task　profit　and　service　latency　cost,under　the　restriction　of　system　timeout　as　well　as　processing　resource.　Then,a　policy　gradient　based　task　offloading　(PG-TO)　algorithm　is　proposed　to　solve　the　optimization　problem.　Finally,the　numerical　result　shows　that　the　proposed　PG-TO　has　better　performance　than　the　comparison　algorithm,and　the　system　performance　as　well　as　QoS　is　analyzed　respectively.　The　testing　result　indicates　that　the　proposed　method　has　good　generalization.　©　2023　Inst.　of　Scientific　and　Technical　Information　of　China.　All　rights　reserved.