This paper considers the admissible consensus problem of discrete-time descriptor multi-agent systems with distributed observer-based control protocols. The dynamics of the agents is assumed to be discrete-time linear descriptor systems, and the interaction topology is assumed to be fixed and directed. By assumption that the agent's states can not be available directly, a dynamical state-observer modeled by a normal liner system is adopted by each agent, by which the related consensus protocols are constructed. Based on the modified generalized discrete-time Riccati equation and Lyapunov admissible theory, a sufficient admissible consensus condition is established. Our design approach provides a general framework, which includes the full-order and reduced-order observer-based consensus design methods. Some full-order and reduced-order observer-based consensus protocols can be obtained by solving the established conditions. Finally, a simple simulation example is provided to illustrate our established result.