Unmanned aerial vehicle (UAV) working as an aerial station can gather the instantaneous information to guarantee the low-latency communication for the smart grid network. In this paper, we firstly construct a practical model of the end-to-end delay with considering the bit-error-ratio (BER) requirement of the communication link, and optimize the UAV’s trajectory to minimize the end-to-end delay between the UAV and the smart grid terminals, in which the critical-mission terminals (CMTs) or non-critical-mission terminals (NCMTs) send the individual information to the flying UAV. Although this non-convex problem is difficult to solve, we propose a trajectory design scheme based on Q-learning. To reduce the delay of CMTs, we design the different reward function for CMTs and NCMTs. The promising advantage of proposed scheme is that some NCMTs closed to CMTs may obtain the priority service to reduce the waiting delay. Simulation results show that our proposed scheme obtains almost 17% performance gain comparing to the benchmark schemes.