To solve the tracking problems of communication delay and parameter uncertainty in spacecraft formation flying system and realize the control objective of collision avoidance, this study investigated the adaptive cooperative control of spacecraft formation flying system with collision avoidance based on the relative motion nonlinear dynamic model and the potential function method. First, an adaptive cooperative collision avoidance control law with full state feedback was proposed, which has the robustness to communication delays and parameter uncertainties. Then, considering the situation of unmeasurable velocity, a control law without velocity measurement was proposed by introducing a new type of filter, which can enable the formation spacecraft to track the desired trajectory and fly in the safe regions without collision. Finally, the Lyapunov stability of the spacecraft formation flying closed-loop system was analyzed for the cases of full state feedback and without velocity measurement feedback, and it was found that the robustness of the closed-loop system to communication delay and parameter uncertainty was significantly improved. Simulation results show that the proposed two adaptive cooperative control laws could guarantee that the formation spacecraft tracks the desired trajectory effectively and achieves the formation flying mission with collision avoidance.