In this work, we investigate a trajectory design problem in uplink unmanned aerial vehicles (UAVs)-enabled data collection system for massive time-sensitive Internet of Things (IoT) services. Although UAV has the advantages of automatic maneuverability and flexible mobility, it is challenging to guarantee the information freshness of collected data under the limited flying energy constraint. Thus we employ Age of Information (AoI) as a new metric to characterize the information freshness and formulate a joint power control and trajectory design optimization problem to minimize average AoI. In order to solve this non-convex problem, we decompose it as a power control subtask and trajectory design subtask, and propose a multi-agent deep reinforcement learning (DRL)-based scheme to solve the subtasks with independent state space, action space and reward function. Simulation results show that the proposed scheme can obtain better performance gain compared to the benchmark scheme and has the superior stability under different settings.