As the computing capacity of existing mobile devices cannot fully meet the needs of users for communication quality, a computing resource allocation strategy for 5G communication in the Internet of Things (IoT) environment is proposed by applying UAV-assisted edge computing. First, a system model is constructed with the UAV deployed with mobile edge computing (MEC) servers to provide assisted computing services for multiple users on the ground. Based on the optimization of the UAV trajectory, communication scheduling, and the energy consumption model of the UAV, the problem of the total computational cost minimization is formulated. Then, the genetic algorithm is improved by introducing a penalty function to solve this problem, in which selection, crossover, and mutation operations are iterated to obtain the optimal allocation strategy for computational resources. Finally, a simulation platform is constructed to analyze the proposed method. The results show that the total cost and total time of the proposed strategy are better than other comparison strategies.