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• Firstly, a robust discrete-time non-smooth consensus protocol solves that consensus problem for the first-order leaderless multi-agent systems with external disturbance and discrete-time feedback. • Then, a discrete-time super-twisting observer is proposed to estimate the multi-agent systems disturbance. Combining the robust discrete-time non-smooth consensus protocol and discrete-time super-twisting observer, we get a new consensus protocol. The superiorities of this method contains two aspects, i.e., the disturbance rejection ability and a smaller consensus error. To the best authors' knowledge, the presented results in this paper are novel in the literature. In this paper, we firstly consider the consensus problems of first-order leaderless multi-agent systems with external disturbance. Then, we propose a robust discrete-time non-smooth (RDTNS) consensus protocol, which makes agents reach consensus within a region. Besides, we design a disturbance observer based on the discrete-time super-twisting algorithm (DTSTA), which can improve the disturbance rejection ability and decrease the consensus error for the multi-agent systems. At last, we get a robust discrete-time disturbance rejection control consensus protocol by combining the RDTNS consensus protocol with the discrete-time super-twisting observer (DTSTO). The simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]