This paper is concerned with trajectory planning for unmanned aerial vehicle in a three-dimensional complex workspace. Biogeography-based optimization algorithm is widely used in solving practical problems because of its fewer parameters, fast convergence rate, and good global optimization ability. In this paper, some improvements, modifying migration and mutation operations are made on the biogeography-based optimization algorithm to make it suitable for solving the trajectory planning problem. The optimal trajectory obtained by the improved algorithm can be used to generate the reference trajectory. Then, a control scheme of unmanned aerial vehicle based on the Lyapunov theory and radial basis function neural network is formed to track the reference trajectory. The improved trajectory algorithm generates the shortest trajectory and the time consumption is the lowest. Finally, the designed control scheme makes the unmanned aerial vehicle track the different trajectories quite well, the effectiveness of it can be illustrated by algorithm accuracy and electricity consumption.