Abstract: Aimed at the task offloading problem in multi-user MEC system equipped with energy harvesting equipment, an online computation offloading strategy is proposed. Lyapunov optimization was utilized to transform the original stochastic optimization problem, so as to calculate the best CPU frequency and transmit power of the mobile devices in each time slot. The simulated annealing algorithm combined with the greedy strategy was used to find the best execution position of the tasks. The experimental results show that compared with the two strategies of task execution completely locally and greedy selection of execution position, the proposed algorithm reduces the system execution cost by 44.1% and 20.3% respectively; compared with the traditional LODCO algorithm and SDTO algorithm, task offloading rate increase by 7.3 and 4.1 percentage points respectively, ensuring the user's QoE.