Aiming　at　the　the　characteristic　of　dependency　relationship　existing　among　multiple　tasks,　a　resource　allocation　strategy　for　multi-task　mobile　edge　computing　systems　is　investigated　in　this　paper.　Sequential　dependency　relationship　among　multiple　tasks　is　taken　into　account.　When　the　current　task　completes　offloading,　the　next　task　can　be　offloaded　without　waiting　for　the　current　task　to　finish　computing.　By　using　a　two-tier　offloading　strategy,　when　the　edge　server　in　small　base　station　has　insufficient　computing　capacity,　the　offloading　task　could　be　further　divided　and　offloaded　to　the　edge　server　in　macro　base　station　with　sufficient　computation　resources.　The　resource　allocation　problem　is　formulated　as　an　optimization　problem.　The　objective　is　to　minimize　the　total　computation　time　of　the　overall　system　under　the　constraints　of　computing　capability　range　of　user,　maximal　computing　resource　of　edge　server,　and　maximal　transmitting　power　of　user.　To　solve　the　formulated　optimization　problem,　a　suboptimal　solution　is　obtained　by　adopting　a　quantum-behaved　particle　swarm　optimization　(QPSO)　algorithm.　Simulation　results　show　that　the　performance　of　the　proposed　strategy　is　superior　to　other　benchmark　strategies,　and　QPSO　algorithm　has　less　computation　time　compared　with　the　standard　particle　swarm　optimization　algorithm.