Unmanned aerial vehicle (UAV)-enabled mobile-edge computing (MEC) is expected to provide low-latency, ultrareliable, and highly robust network services to improve user service experience. In this article, the UAV deployment, task offloading, and resource allocation problem is investigated in a multi-UAV-enabled MEC system with task-intensive region. UAVs as edge servers to provide computing services for ground terminal devices (TDs). The time-sensitive tasks of TDs can be computed locally or offloaded to UAVs. The goal is to improve the utility of tasks, i.e., maximize the number of tasks offloaded to UAVs under conditions of ensuring a desired task computed success rate and satisfying the energy and latency constraints. The jointly optimizing problem of the 3-D deployment, elevation angle, computational resource allocation of the UAV, and task offloading decision is formulated. To this end, a two-layer optimization approach is proposed to solve the formulated problem. Specifically, the upper layer decides the UAV position, elevation angle, and transmission power of TDs based on the actual ground situation. The lower layer determines the computational resource allocation of UAVs and the task offloading decision based on the optimized results derived from the upper layer. Through the two-layer joint optimization, our goal is finally achieved. Simulation results demonstrate that our proposed algorithm effectively improves the number of tasks offloaded to UAVs and the task completion rate simultaneously with the flexible UAV deployment and well-designed task offloading strategy.