Dead-zone nonlinearities are a kind of common nonlinear characteristics of the actuator nonlinearities of spacecraft attitude control systems. They could degrade the performance, and even lead to un-stability of spacecraft attitude control systems. To solve the high precision attitude control problem for spacecraft with input dead-zone nonlinearities, this paper proposes a kind of finite time control approach. The attitude control model of the spacecraft considered in this paper is with bounded uncertainties and the information of the input dead-zone nonlinearities is only partially known. A desired attitude curve which converges to zero in the given time is introduced. A robust finite-time control algorithm is proposed based on the time-varying sliding mode approach to ensure the error between the actual attitude and the desired one keep small enough all the time. This further ensures that the actual attitude converges to the nearby of zero in the given time. By rigorous analysis, it is proved in theory that all of the signals in the closed-loop system are bounded and the attitude error can be driven into a small given neighborhood of the origin in the pre-specified time and stay there thereafter. The numerical simulation results show that the proposed control method is effective. It could guarantee that the system possesses fast state convergence speed, high control precision, and good robustness with respect to uncertainties and disturbances, so it has good potential application value in the attitude control of spacecraft.