In this paper, we investigate the joint problem of task offloading, Unmanned Aerial Vehicle (UAV) trajectory design, and resource allocation for UAV-enabled edge computing, considering and highlighting the dependency among different tasks. The corresponding optimization problem, which is a mixed-integer problem, is formulated. To solve this problem, we propose an iterative method based on Block Coordinate Descent (BCD) to decompose the original problem into two subproblems. Given the offloading decision and resource allocation, the subproblem of UAV trajectory optimization is solved by convex optimization methods. Then, given the UAV trajectory, the subproblem of task offloading decision and the corresponding resource allocation is solved by dynamic programming and convex optimization methods. Simulation results show that our proposed method can significantly reduce energy consumption compared to the benchmark schemes.