This paper proposes a finite-time consensus control algorithm based on nonlinear integral sliding-mode control for second-order multi-agent systems (MASs) with mismatched and matched disturbances. Firstly, a nonlinear finite-time disturbance observer is established to estimate the states and mismatched disturbances of the agent. Secondly, a dynamic integral sliding-mode (ISM) surface is designed by employing the estimates of mismatched disturbances. Then, based on the designed ISM and disturbance observer, the discontinuous or continuous campsite control protocols are respectively developed to guarantee the consensus for MASs in finite time with active anti-disturbance control. Finally, numerical simulation results illustrate the effectiveness of the proposed consensus control algorithm.