In order to solve the problems of high sampling and search randomness, poor environmental adaptability and unsmooth planning path of bidirectional RRT* algorithm in the process of UAV global path planning in complex environments, this paper proposes a bidirectional fast stochastic tree star path planning algorithm (FB-RRT*) that integrates step size strategy. Firstly, in order to solve the problem of high sampling randomness, a sampling strategy with target bias is set up to reduce the number of blind random samples. Then, the dynamic random step size of the fusion angle and obstacle environmental parameters is used to improve the environmental adaptability of the algorithm. Finally, in order to solve the problem of too long planned path, the path clipping and B-spline optimization strategy are combined to effectively remove the redundant turning points, so as to obtain a better path. MATLAB experimental results show that compared with the B-RRT* algorithm, the average planning time is reduced by 58% and the average path length is shortened by 11.9%, which shows that the improved FB-RRT* algorithm has efficient planning ability.