Most of existing works related to mobile edge computing (MEC) focused on the total energy consumption or task completion time. However, for the applications with multiple players as a whole, the diverse battery levels of players should be considered to achieve better quality of experience (QoE), which is reflected in the metrics of task completion time and the lifespan of service. In this paper, we focus on QoE and diversity of devices. By jointly considering the individual battery level of different devices, we formulate an optimization problem to minimize the task completion time of the system. Firstly, we propose two necessary conditions to achieve the optimal solution of the formulated problem. In addition, we transform the formulated problem into another problem, which can be used to judge whether a given value is feasible for the formulated problem based on the proposed optimal conditions and bisection searching (BSS) algorithm. Then, we propose a method named sub-channel (SC) matching based on virtual computation resource (SMVCR) to solve the transformed problem with low computational complexity. Simulation results indicate that the BSS-SMVCR algorithm has a good performance in task completion time compared with some existing algorithms, and also can significantly extend the lifespan of the corresponding service, which is reflected in the supporting number of offloading tasks.