Mobile Edge Computing (MEC) servers receive revenue by leasing computing resources to users. Improving revenue with limited computing resources is critical for MEC servers. Therefore, a strategy of improving MEC server revenue by the optimization of computing task execution order was proposed. Firstly, the revenue maximization problem of servers was modeled to an optimization problem with task execution order as optimization parameter. Then, an algorithm based on the branch and bound approach was proposed to find the optimal task execution order. Simulation results show that the average revenue of MEC server of the proposed algorithm is 11%, 14% and 21% higher than those of Large Task First (LTF) algorithm, Low-Latency Task First (LLTF) algorithm, and First Come First Served (FCFS) algorithm respectively. The proposed strategy can significantly improve the servers’ revenue while guaranteeing offloading users’ Quality of Service (QoS).