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In a single UAV-assisted mobile edge computing system, in order to enable the UAV to serve all user devices in a large area, the large area can be divided into a plurality of sub-areas and the UAV can be set to fly between the sub-areas with a fixed route to provide computing services for the user devices. Considering the scarcity of computational resources for user devices and the fact that users outside the coverage area of the UAV may choose to move to the coverage area for task offloading in order to maximize their own utility, the partial offloading problem of user devices can be transformed into the problem of maximizing the utility of each user device. The mixed-strategy game and the submodular game are used to determine the movement probability of user devices and the amount of offloaded data, so as to derive the optimal offloading strategy, and the existence of mixed-strategy Nash equilibrium and pure-strategy Nash equilibrium is proved, respectively. Simulation results show that the proposed scheme can effectively improve the utility of user device compared with classical schemes such as MBO (Binary Offloading Based on Mixed Strategy Game), and its convergence and stability are verified.