In this paper, the attitude control problem of rigid body is addressed with considering inertia uncertainty, bounded time-varying disturbances, angular velocity-free measurement, and unknown non-symmetric saturation input. Using a mathematical transformation, the effects of bounded time-varying disturbances, uncertain inertia, and saturation input are combined as total disturbances. A novel finite-time observer is designed to estimate the unknown angular velocity and the total disturbances. For attitude control, an observer-based sliding-mode control protocol is proposed to force the system state convergence to the desired sliding-mode surface; the finite-time stability is guaranteed via Lyapunov theory analysis. Finally, a numerical simulation is presented to illustrate the effective performance of the proposed sliding-mode control protocol.