Edge　computing　is　an　emerging　promising　computing　paradigm　that　brings　computation　and　storage　resources　to　the　network　edge,　significantly　reducing　service　latency.　In　this　paper,　we　aim　to　divide　the　task　into　several　sub-tasks　through　its　inherent　interrelation,　guided　by　the　idea　of　high　concurrency　for　synchronization,　and　then　offload　sub-tasks　to　other　edge　servers　so　that　they　can　be　processed　to　minimize　the　cost.　Furthermore,　we　propose　a　DRL-based　Multi-Task　Dependency　Offloading　Algorithm　(MTDOA)　to　solve　challenges　caused　by　dependencies　between　sub-tasks　and　dynamic　working　scenes.　Firstly,　we　model　the　Markov　decision　process　as　the　task　offloading　decision.　Then,　we　use　the　graph　attention　network　to　extract　the　dependency　information　of　different　tasks　and　combine　Long　Short-term　Memory　(LSTM)　with　Deep　Q　Network　(DQN)　to　deal　with　time-dependent　problems.　Finally,　simulation　experiments　demonstrate　that　the　proposed　algorithm　boasts　good　convergence　ability　and　is　superior　to　several　other　baseline　algorithms,　proving　this　algorithm’s　effectiveness　and　reliability.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.