In this paper, when actuator failure occurs, an adaptive fault-tolerant control (AFTC) strategy is proposed to solve the problem of attitude tracking control and vibration suppression in a flexible satellite system described by an ODE–PDE interconnected system. The moment of inertia matrix of the system and which actuator fails and when the failure occurs are unknown. To solve these problems, an adaptive control strategy is designed based on uncertainty parametrization and symmetric positive definite matrix–diagonal matrix–unit upper triangular matrix (SDU) factorization. The modified Lyapunov method and the assumed mode principle are used to prove that attitude tracking and vibration suppression can be realized. Finally, the simulation results show that AFTC strategy can be realized and is effective.