In this paper, the finite-time output consensus problem is considered for a class of second-order multiagent systems (MASs), where the mismatched disturbance exists in the dynamics of each agent, and the communication topology is directed. First of all, a basic backstepping control protocol is proposed to solve the finite-time consensus problem without mismatched disturbance. Then, a finite-time disturbance observer is designed to estimate the mismatched disturbance, based on which, two adaptive finite-time consensus protocols are proposed to solve the finite-time output consensus and tracking consensus problems without using any global information with respect to the communication topology. Finally, two simulation examples are illustrated to verify the theoretical results.