Reasonable path planning of a mobile robot in operation is a key to completing the task safely and efficiently. Such a path planning often needs to be done base only on a given environment that is unknown to the Agent at the beginning, and an effective reinforcement learning is required. This paper presents Smoothed-Jump Q-Learning (SJQL) Algorithm that enable the Agent to learn and then figure out a smoothed short-cut path to the final goal that is initially unknown to the Agent in a given environment. The SJQL algorithm includes three new solutions: First, a virtual rectangular environment boundary of the environment is constructed, based on the starting point and target point (found by a Q-Learning algorithm). The Q values of guidance for the virtual rectangular environment is increased to improve the learning efficiency of the Agent, and a safe distance matrix is ​​created around the obstacle to improve the security of the path. Second, the path found by the Agent is optimized to achieve the purpose of eliminating the redundant path, reducing the path turning point and shortening the length of the path. Third, at the turning positions on the path, the Bezier curve is used to further smooth the path, so as to improve the dynamics for the movement of the robot Agent. The research results show that the final path generated by our SJQL algorithm will be optimal in terms of fast convergence, smoothness and shortest distance, and it can ensure the smoothness and safety of the mobile robot working along the planned path.