With the development of Unmanned Aerial Vehicles (UAV) and cellular networks, path planning for cellular-connected UAV has become a very popular research area. Previous researches on path planning for cellular-connected UAV focused on point-to-point path planning which can be solved by estimate approximate Shortest Path Problem (SPP). However, cellular-connected UAV has extra constraints that it must keep a good connection with Ground Base Stations (GBS) at all times to make the UAV stay in control, thus make the problem more challenging. In this paper, we studied path planning for cellular-connected UAV in a specific scenario where UAV have to visit multiple points while keeping connected with GBSs and get back to where it starts finally. In other words, we want to study multi-points path planning which can be abstracted as Travel Salesman Problem (TSP). In order to solve this kind of problem, a reinforcement learning based model has been proposed and developed and the experiment results of our model have proved that it can solve the UAV path planning problem with a good performance.