Recently, research intergrading medicine and Artificial Intelligence has attracted extensive attention. Mobile health has emerged as a promising paradigm for improving people’s work and life in the future. However, high mobility of mobile devices and limited resources pose challenges for users to deal with the applications in mobile health that require large amount of computational resources. In this paper, a novel computation offloading mechanism is proposed in the environments combining of the Internet of Vehicles and Multi-Access Edge Computing. Through the proposed mechanism, mobile health applications are divided into several parts and can be offloaded to appropriate nearby vehicles while meeting the requirements of application completion time, energy consumption, and resource utilization. A particle swarm optimization based approach is proposed to optimize the aforementioned computation offloading problem in a specific medical application. Evaluations of the proposed algorithms against local computing method serves as base line method are conducted via extensive simulations. The average task completion time saved by our proposed task allocation scheme increases continually compared with the local solution. Specially, the global resource utilization rate increased from 71.8% to 94.5% compared with the local execution time.