In recent years, Mobile Edge Computing (MEC) and Wireless Power Transfer (WPT) technologies have been widely applied to wireless devices (WDs). However, in remote areas or during disaster events, data and energy transmission cannot be accomplished through conventional ways. To address this challenge, this paper explores a WPT-MEC system using Unmanned Aerial Vehicle (UAV) with 3D flying and obstacle avoidance. Our goal is to maximize the long-term task completion ratio while considering the constraints of UAV coverage, time resources, energy, and task validity duration. We first model this problem into multiple equal-sized time slots, with each time slot involving two main actions. The first action is the UAV selecting its flight direction based on the tasks of the on-site WDs. The second action is after UAV’s flying, the WDs which are in the UAV’s coverage offload their tasks to UAV. For each action decision, we design a Deep Reinforcement Learning (DRL) algorithm. By training two models to accomplish this task, our algorithm significantly improves the long-term task completion ratio, with performance improvements reaching up to 40% in certain scenarios compared to baseline methods.