This paper proposes a task offloading and resource allocation algorithm based on mobile edge computing. Firstly, for the long-term performance optimization of small base stations, the system model is established according to task arrival characteristics, credit relationship between small base stations, time delay and energy consumption of computing tasks and cable channel congestion. Secondly, the energy consumption deficit queue based on Lyapunov drift penalty technology used for the energy consumption constraint of small base stations in long-term optimization process. The energy consumption deficit queue is established for each small base station to couple the energy consumption and time of small base stations, so that small base stations can meet the energy consumption constraints in longterm optimization process. Finally, game theory is introduced to calculate offloading weight by the offloading weight model based on Shapley value. Besides, the offloading weight is calculated equitably according to the return of different tasks. Simulation results on MAT-LAB platform show that the proposed algorithm can achieve Nash equilibrium after finite iterations. Moreover, its performance on energy consumption, time delay and number of tasks successfully offloaded is better than other comparison strategies.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.