Unmanned aerial vehicle (UAV)-assisted mobile communication has been studied in recent years. UAVs can be used as aerial base stations (BSs) to improve the performance of terrestrial mobile network. In this article, mobile data offloading with UAV trajectory optimization is investigated. To tackle with the delay of requesting data and the immediacy of requested data at the same time, a new metric named delanalty is newly proposed. The delanalty metric jointly considers the delay of user requesting data, the immediacy of requested data file, and the quantity of residual requesting data. A find max delanalty user mechanism is proposed to eliminate the user who has the largest delay time. Furthermore, an actor–critic (AC)-based deep reinforcement learning (DRL) algorithm called AC -based delanalty trajectory optimization (ACDTO) algorithm is proposed to solve UAV’s trajectory optimization problem. Simulation results show that the proposed ACDTO algorithm can find an optimal flight trajectory with minimal delanalty for all users.