To solve the long training time and slow convergence problems when applying SAC （Soft Actor-Critic） algorithm to the local path planning of mobile robots， a PER-SAC algorithm was proposed by introducing the Prioritized Experience Replay （PER） technique. Firstly， to improve the convergence speed and stability of the robot training process， a priority strategy was applied to extract samples from the experience pool instead of the traditional random sampling and the network prioritized the training of samples with larger errors. Then， the calculation of Temporal-Difference （TD） error was optimized， and the training deviation was reduced. Next， the transfer learning was used to train the robot from a simple environment to a complex one gradually in order to improve the training speed. In addition， an improved reward function was designed to increase the intrinsic reward of robots， and therefore， the sparsity problem of environmental reward was solved. Finally， the simulation was carried out on the ROS （Robot Operating System） platform， and the simulation results show that PER-SAC algorithm outperforms the original algorithm in terms of convergence speed and length of the planned path in different obstacle environments. Moreover， the PER-SAC algorithm can reduce the training time and is significantly better than the original algorithm on path planning performance.