This technical note studies the finite-time consensus problem of leader-follower higher-order multi-agent systems with mismatched disturbances. To solve such a problem, by combining the non-singular terminal sliding-mode control (NTSMC) and disturbance observer based control (DOBC) methods together, a distributed active anti-disturbance cooperative control scheme is proposed. Firstly, to estimate the matched/mismatched disturbances of each follower, a finite-time disturbance observer is constructed. Secondly, by distributedly employing the mismatched disturbances estimates, integral-type non-singular terminal sliding-mode surfaces are designed for followers. Thirdly, distributed protocols are proposed based on the surfaces. In the presence of mismatched disturbances, these protocols achieve finite-time output consensus for the agents. Simulations validate the correctness and effectiveness of the proposed control scheme.