Wireless Body Area Network (WBAN) as one of the primary Internet of Things (IoT) provides real time and continuous healthcare monitoring and has been widely deployed to improve the quality of peoples' life. In edge-enabled WBANs, intensive computing tasks could be offloaded to Mobile Edge Computing (MEC) servers, guaranteeing that the massive amount of health data with different user priorities could be processed in lower delay and energy consumption. Efficient computation offloading schemes are more critical to satisfy the massive data access and personalized service requirements for multiple Quality of Service (QoS) parameters constraint WBANs. In this paper, we propose a Two-Stage Potential Game based Computation Offloading Strategy (TPOS) to optimize resource allocation while taking into consideration the task priorities and user priorities of WBANs. Firstly, we construct a system utility maximization problem about the QoS of tasks. The reward, cost and penalty functions are given to model the computation offloading. Then, we propose a two-stage optimization method to solve the problem of mutual restriction strategies existing in the strategy space of the potential game model, reducing the computation complexity and improving the feasibility of the algorithm. Finally, performance evaluations on average processing delay, energy consumption and network utility are conducted to show the significance of the proposed TPOS algorithm. INDEX TERMS WBAN, edge computing, computation offloading, potential game, healthcare monitoring.