Aiming at the problem of large system overhead and obvious delay jitter when offloading intensive tasks in Mobile Edge Computing (MEC), a new resource allocation strategy is proposed. Firstly, the strategy analyzes the system's task execution overhead and the terminal equipment's resource allocation mechanism under the constraints of system delay. Secondly, a joint convex optimization pro- blem of computation offloading and task assignment is established. Finally, the Lagrangian multiplier method is used to yield the optimal solution by iterative updating. The simulation results show that the proposed task offloading and resource allocation strategy ensures the user's quality of service while reducing the task execution overhead and effectively improves the performance of the MEC system.