Swarm control has become a challenging topic for the current unmanned aerial vehicle (UAV) swarm due to its conflicting individual behaviors and high external interference. However, in contrast to static obstacles, limited attention has been paid to the fission–fusion behavior of the swarm against dynamic obstacles. In this paper, inspired by the interaction mechanism and fission–fusion motion of starlings, we propose a Bio-inspired Self-organized Fission–fusion Control (BiSoFC) algorithm for the UAV swarm, where the number of UAVs in the sub-swarm is controllable. It solves the problem of swarm control under dynamic obstacle interference with the tracking function. Firstly, we establish the kinematic equations of the individual UAV and swarm controllers and introduce a fission–fusion control framework to achieve the fission–fusion movement of the UAV swarm with a lower communication load. Afterward, a sub-swarm selection algorithm is built upon the topological interaction structure. When a swarm is faced with different tasks, the swarm that can control the number of agents in a sub-swarm can accomplish the corresponding task with a more reasonable number of agents. Finally, we design a sub-swarm trapping algorithm with a tracking function for the dynamic obstacles. The simulation results show that the UAV swarm can self-organize fission sub-swarms to cope with dynamic obstacles under different disturbance situations, and successfully achieve the goal of protecting the parent swarm from dynamic obstacles. The experimental results prove the feasibility and effectiveness of our proposed control algorithm.