The process of formation reconfiguration for close-range satellite formation should take into account the risk of collisions between satellites. To this end, this paper presents a method to rapidly generate low-thrust collision-avoidance trajectories in the formation reconfiguration using Finite Fourier Series (FFS). The FFS method can rapidly generate the collision-avoidance three-dimensional trajectory. The results obtained by the FFS method are used as an initial guess in the Gauss Pseudospectral Method (GPM) solver to verify the applicability of the results. Compared with the GPM method, the FFS method needs very little computing time to obtain the results with very little difference in performance index. To verify the effectiveness, the proposed method is tested and validated by a formation control testbed. Three satellite simulators in the testbed are used to simulate two-dimensional satellite formation reconfiguration. The simulation and experimental results show that the FFS method can rapidly generate trajectories and effectively reduce the risk of collision between satellites. This fast trajectory generation method has great significance for on-line, constantly satellite formation reconfiguration.