With the development of computation-intensive applications, unmanned aerial vehicle (UAV)-enabled multi-access edge computing (MEC) provides task offloading service for the users with or without terrestrial infrastructure support. Meanwhile, the next generation of UAVs communication systems are expected to be user-centric. Therefore, more attention should be paid to users’ satisfaction with the offered service. In this paper, we study the service satisfaction-oriented task offloading and UAV scheduling problem for UAV-enabled MEC networks, where the task priorities are considered based on the delay requirements of users’ tasks and the remaining energy status of users. Specifically, we firstly divide the users into different groups via the K-means-based grouping algorithm. Then, we develop a novel user satisfaction model by jointly considering the task processing delay and energy saving, based on which a total user satisfaction maximization problem is formulated to jointly optimize the task offloading decisions and UAV scheduling strategy. To solve the formulated problem, we decompose it into two sub-problems, i.e., the UAV scheduling sub-problem and the task offloading sub-problem. To solve the first sub-problem, we develop a genetic algorithm (GA)-based UAV scheduling algorithm through dealing with multiple balanced assignment problems. To address the second sub-problem, a GA-based task offloading algorithm is developed. Then, we propose a joint task offloading and UAV scheduling optimization algorithm to solve the original optimization problem. Finally, simulation results demonstrate that the proposed optimization algorithm not only converges fast, but also improves the total users’ satisfaction greatly. The total users’ satisfaction improved by the proposed scheme is up to 16.9% in the case of 170 users.