With the development of the smart Internet of things (IoT) system, the type and number of applications in the IoT continue to increase. In mobile edge computing (MEC), mobile applications are accelerated by allowing mobile users to offload tasks to nearby MEC servers. This study simulates mobile edge scenarios by analyzing task attributes, user mobility, and delay constraints. In addition, according to the moving trajectory of users, the goal is modeled. Specifically, it aims to find an optimization model for MEC servers that satisfies the delay constraints and generates the minimum energy consumption during the offloading. The study also proposes a minimum energy offloading algorithm to find the optimal solution to this problem. The simulation results show that under the constraints, the proposed algorithm can find a MEC server that generates the minimum energy consumption in the moving trajectory of users, significantly reduce the energy consumption and delay during task offloading, and improve the application service quality.