In this paper, a fully distributed control algorithm is proposed to eliminate the dependence of formation system on global information for the cooperative control of fully distributed quadrotor unmanned aerial vehicle (UAV) formation. Firstly, using the idea of double closed-loop control, a fully distributed PD controller is designed for the outer loop position tracking subsystem based on the PD control algorithm, enabling formation members to track the expected trajectory and maintain the preset formation configuration during the tracking process. For the inner loop attitude control subsystem, the sliding mode control theory and LMI control algorithm are used to design the attitude controller to track the desired attitude signal output from the outer loop system. In addition, the double closed-loop system is compensated for external disturbances using adaptive laws. Then, based on Lyapunov stability theory, it is proven that the system tracking error can reach a stable state. Finally, the effectiveness of the fully distributed formation controller was verified through numerical simulation results.