This paper deals with output feedback consensus problem for second-order multi-agent systems with heterogeneous nonlinearities and disturbances. A novel distributed observer is first designed for each agent to estimate its velocity information in finite time when there exist Lipschitz-type nonlinearity and bounded disturbance simultaneously. Then based on the observers and homogenous method, a new finite-time consensus protocol is proposed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed protocol.