Unmanned aerial vehicles (UAVs) have been widely used in wireless communication systems because of their flexibility and maneuverability. In this paper, for more efficient computing services, we consider computing tasks offloading in an air-ground system that a ground base station (GBS) and a UAV cooperatively serve the ground users. Our goal is to minimize the total transmission energy consumptions of the ground users by jointly optimizing the multi-user offloading strategy and the UAV's trajectory, while ensuring UAV's mobility and task delay constraints. This problem includes non-convex objective function, binary variables and non-convex constraints. Therefore, we transform the original problem into two tractable subproblems by introducing the auxiliary variables and relaxing the binary variables. Furthermore, we propose an alternative optimization algorithm to handle these sub-problems. Simulation results illustrate that our proposed algorithm can significantly reduce the total transmission energy consumptions of the ground users.