In this paper, we investigate resource allocation design for unmanned aerial vehicle (UAV)-enabled communication systems, where a UAV is dispatched to provide communications to multiple user nodes. Our objective is to maximize the communication system throughput by jointly optimizing the subcarrier allocation policy and the trajectory of the UAV, while taking into account the minimum required data rate for each user node, no-fly zones (NFZs), the maximum UAV cruising speed, and initial/final UAV locations. The design is formulated as a mixed integer non-convex optimization problem which is generally intractable. Subsequently, a computationally-efficient iterative algorithm is proposed to obtain a locally optimal solution. Simulation results illustrate that the performance of the proposed iterative algorithm approaches closely to that of the system without NFZ. In addition, the proposed algorithm can achieve a significant throughput gain compared to various benchmark schemes.