In this paper, the finite-time output feedback stabilization problem for a kind of second-order system with mismatched disturbances is investigated. To estimate both the unknown states and the disturbances in such a system, a finite-time convergent observer is designed. Based on homogeneous control technique and the designed observer, an output feedback composite controller is proposed. The developed controller globally finite-time stabilizes the disturbed system. Furthermore, the composite control method is used to solve the finite-time consensus problem of the leaderless second-order systems with mismatched disturbances. Simulation results demonstrate the effectiveness of the proposed control algorithms.