This paper addressed a well-documented open problem regarding multiple unmanned aerial vehicles (multi-UAVs) formation keeping. A cooperative guidance control method based on the back-stepping approach is proposed to rapidly form the desired formation and reach the multi-UAV steady state. The UAV formation system consists of four UAVs, forming a regular triangle formation. One of the UAVs is a virtual leader and is located at the center of the triangle; the other three UAVs are located at the vertices of the triangle. The forward speed of leader is used as the forward direction of the formation, and the followers follow the leader in a formation flight. The error dynamics model of each follower is established by using the leader guidance mechanism, and the communication mode between any two UAVs is established based on graph theory. In addition, the guidance control law is obtained via the back-stepping approach. We reasonably construct the Lyapunov function to prove the stability of the proposed cooperative guidance control law in formation aggregation and keeping. Moreover, the proposed method is compared with the model prediction method (MPC) and the Lyapunov method to further verify the effectiveness of the proposed method. The simulation results show that each UAV can converge to the desired motion trajectory and fly in the desired formation with fast convergence speed and small steady-state error.