A backstepping method is used for nonlinear spacecraft attitude stabilization in the presence of external disturbances and time delay induced by the actuator. The kinematic model is established based on modified Rodrigues parameters(MRPs).Firstly, we get the desired angular velocity virtually drives the attitude parameters to origin, and then backstep it to the desired control torque required for stabilization. Considering the time delay induced by the actuator, the control torque functions only after the delayed time, therefore time compensation is needed in the controller. Stability analysis of the close-loop system is given afterwards. The infinite dimensional actuator state is modeled with a first-order hyperbolic partial differential equation(PDE), the L2 norm of the system state is constructed and is proved to be exponentially stable. An inverse optimality theorem is also employed during controller design. Simulation results illustrate the efficiency of the proposed control law and it is robust to bounded external disturbances and time delay mismatch. A kinematic model is established based on modified Rodrigues parameters (MRPs). Firstly, we get the desired angular velocity virtually drives the attitude parameters to origin, and then backstep it to the desired control torque required for stabilization. the control torque functions only after the delayed time, therefore time compensation is needed in the controller. -loop system is given afterwards. The infinite dimensional actuator state is modeled with a first-order hyperbolic partial differential equation (PDE), the L2 norm of the system state is constructed and is proved to be exponentially stable. An inverse optimality theorem is also employed during controller design. Simulation results illustrate the efficiency of the proposed control law a nd it is robust to bounded external disturbances and time delay mismatch.