The state consensus problem of high-order discrete-time linear multi-agent system(HDLMAS) under a directed switching information topology is investigated. Firstly, a proper linear transformation is proposed to transform the consensus problem to the asymptotic stability problem of a corresponding discrete-time linear switched system(DLSS). Then for the following two cases, sufficient conditions for the solvability of the consensus problem are deduced by using the average dwell-time approach of DLSS, respectively: 1) some in a given set of information topologies are consensusable; 2) all in the given set of information topologies are consensusable. Finally, simulation result shows the correctness of the obtained results.