This paper studies the problem of trajectory design for unmanned aerial vehicle (UAV)-assisted emergency communications, where the ground base station (BS) may be no longer functioning and the UAV acts as an aerial BS to provide emergency communication services to the ground users. In the event of emergency situations, the user distribution and the geographical features of the target area may have changed dramatically while urgent demand for communications are raised by the surviving ground users. In this paper, we model UAV trajectory design problem as a deep reinforcement learning (DRL) process and propose to adopt transfer learning to leverage previously learned knowledge so as to boost up the learning procedure. Simulation results validate that with limited interactions with the environment, the UAV can rapidly and effectively adapt its trajectory to the new environment and achieve much faster convergence speed than DRL based design.