In this paper, the leader-following consensus problem of discrete-time descriptor multi-agent systems is considered. Each agent’s dynamics is modelled by a discrete-time linear descriptor system, and the interaction topology among the agents is assumed to be directed. To solve the multi-agent consensus problem, three different architectures of connecting observers and controllers are used to construct the consensus protocols. A kind of modified generalized algebraic Riccati equation is provided to design the protocol’s gain matrices. Based on graph theory, matrix theory and the Lyapunov method, some sufficient convergence conditions are established to guarantee the descriptor multi-agent system achieves consensus. Finally, a simulation example is provided to illustrate the obtained results.