The motion planning ability of mobile robots are facing a severe challenge with complex environment and less prior information. It is important to study the motion planning method and theory for a mobile robot, so that the mobile robot could adapt to complex environment in a long-running and ensure the work security and task efficiency. This paper mainly summarizes the method based on deep reinforcement learning(DRL) which can deal with the dynamic and complicated obstacles better. The DRL methods, which are based on value, policy and actor-critic, are introduced respectively. Then, the typical robot application in simulation environment and complex real world environment are analyzed based on DRL. After comparing the advantages and disadvantages in detail, the improvement and optimization direction for the DRL method are classified, and the challenges faced by motion planning method are put forward respectively. Finally, the prospects in the field of mobile robot motion planning method with DRL are discussed, which will provide reference for the development of intelligent robots.