Mobile　edge　computing　(MEC)　is　a　promising　approach　that　can　reduce　the　latency　of　task　processing　by　offloading　tasks　from　user　equipments　(UEs)　to　MEC　servers.　Existing　works　always　assume　that　the　MEC　server　is　capable　of　executing　the　offloaded　tasks,　without　considering　the　impact　of　improper　load　on　task　processing　efficiency.　In　this　article,　we　present　a　two-stage　computing　offloading　scheme　to　minimize　the　task　processing　delay　while　managing　the　server　load　properly.　To　minimize　the　task　processing　delay,　each　UE　optimizes　how　much　workload　to　be　offloaded　to　the　MEC　server.　To　improve　the　task　processing　efficiency　of　the　server,　we　arrange　the　processing　order　of　offloading　tasks　by　introducing　an　aggregative　game　with　an　instantaneous　load　billing　mechanism.　The　proposed　game　can　obtain　the　optimal　task　offloading　and　processing　strategy　with　limited　information　and　a　small　number　of　iterations.　Simulation　results　show　that　our　scheme　approaches　the　optimal　offloading　strategy　in　terms　of　minimizing　task　processing　delay　for　each　UE　and　improving　processing　efficiency　for　the　server.