This paper studies the formation containment control algorithm for multiple spacecraft systems under actuator and sensor faults. Firstly, the orbit dynamics of the spacecraft is modeled and linearized. Then, an adaptive descriptor observer is designed to obtain the estimated values of system states as well as actuator and sensor faults. By adjusting the nonsingular matrix, the performance of the observer can be improved and the observer error can converge near the origin. Based on the estimated system states and actuator faults, formation containment controller is designed. The sufficient conditions for the convergence of formation error and observer error are obtained through Lyapunov analysis. Finally, the system performance under the designed algorithm is verified by a simulation example.