Aiming at the influence of the dynamic change of the offloading environment in the vehicle edge computing on the computing offloading, this paper proposes a computing handoff strategy based on Markov decision process. While ensuring the task completion time, the strategy analyzes the overall process of computing offload to further reduce the influence of the handoff strategy on the offloading effect. Simulation experiments are carried out to show that whether the introduction of the switch can improve the computing offloading effect and how the strategy further reduces the influence of the handoff policy strategy on the offloading effect. The experimental results show that, compared with, the proposed handoff strategy can improve the efficiency of computing offloading and ensure the user service experience.