In this paper, the attitude control problem of the spacecraft system under input/state constraints and multi-source disturbances is investigated. A novel estimation method, composite-disturbance-observer (CDO), is proposed to provide an estimate for both modeled and unmodeled disturbances in an online manner. Based on the estimates provided by the CDO, the composite stochastic model predictive control (C-SMPC) scheme is designed for attitude control. The recursive feasibility of the C-SMPC method is guaranteed by reformulating the state and input constraints. Furthermore, the sufficient conditions are established to guarantee the stability of the overall closed-loop system. Finally, the simulation on the attitude control of the spacecraft is conducted to verify the effectiveness of the proposed method.