To improve the reliability of spacecraft system, this paper researches the finite-time output feedback attitude tracking control for rigid spacecraft without angular velocity measurement. The attitude derivative is firstly viewed as an unknown state, and a modified adaptive super-twisting sliding mode state observer is designed and the requirement for the upper bound of unknown state is avoided. By extending dimensions of attitude kinematics equation, the precise angular velocity was estimated in finite time. Then, considering environmental disturbances and system uncertainties, and combining a continuous adaptive approach for estimating the upper bound of system uncertainties, a novel finite-time disturbance observer was designed. Based on the terminal sliding mode, a continuous finite-time attitude tracking controllers is also designed. The control chattering is greatly reduced and the finite-time stability for the observer and the controller is proved via the Lyapunov theory. Finally, simulation results illustrate the effectiveness of the proposed method.