To address the problems of the Rapidly-exploring Random Trees (RRT) algorithm in mobile robot path planning including time cost, long and tortuous path, and poor smoothness, an improved RRT algorithm of new sampling node generation and path node selection is proposed. The algorithm combines the probability of sampling points and the gravitation of the target point, and dynamically changes the random step size, thus accelerating the expansion to the target point and reducing the planning time. Finally, to complete the path optimization, the path nodes obtained after the forward optimization and the secondary selection are processed using the B-spline function, which comprehensively improves the path in terms of length and smoothness. The proposed algorithm has been compared with traditional RRT algorithm and P-RRT algorithm in the simulation experiments, whose results show that the proposed algorithm has improved the path length, planning time and the number of path nodes to a certain amount, and effectively the path smoothness.