In this paper, the finite-time leader-following output consensus problem is investigated for a multi-agent system subjected to directed topology and disturbance. Firstly, a distributed finite-time extended state observer (DFTESO) is designed to provide estimate for unmeasured consensus errors and disturbances. The sufficient condition is provided in terms of linear matrix inequality (LMI) to ensure that the error dynamics of the DFTESO is convergent in finite time. Then, based on the designed observer, the leader-following consensus protocol based on dynamic gain method is proposed under the directed topology. Finally, an example on the multi-spacecraft system is provided to illustrate the effectiveness of the proposed methodology. © 2020 Elsevier Ltd