This article investigates the finite-time attitude stabilization problem by output feedback for a rigid spacecraft without angular velocity measurement. First of all, by employing the finite-time control technique, a finite-time stabilizing controller by state feedback is designed. Then, to address the problem of lack of angular velocity measurement, a semi-global finite-time convergent observer is proposed to recover the unknown angular velocity information in a finite time. Finally, a semi-global finite-time output feedback controller is developed. Rigorous proof shows that the attitude of rigid spacecraft will converge to the equilibrium in a finite time. A simulation example is given to demonstrate the efficiency of the proposed method.