In the course of the task, the mobile robot should find the shortest and most smooth obstacle-free path to move from the current point to the target point efficiently, which is namely the path planning problem of the mobile robot. After analyzing a large number of planning algorithms, it is found that the combination of traditional planning algorithm and heuristic programming algorithm based on artificial intelligence have outstanding performance. Considering that the basic rapidly exploring random tree algorithm is widely used for some of its advantages, meanwhile there are still defects such as poor real-time performance and rough planned path. So, in order to overcome these shortcomings, this article proposes target bias search strategy and a new metric function taking both distance and angle into account to improve the basic rapidly exploring random tree algorithm, and the neural network is used for curve post-processing to obtain a smooth path. Through simulating in complex environment and comparison with the basic rapidly exploring random tree algorithm, it shows good real-time performance and relatively shorter and smoother planned path, proving that the improved algorithm has good performance in handling path planning problem.