Observer design problem is studied mainly for the Lipchitz nonlinear discrete system with time delays in this paper.Some sufficient conditions are obtained for the existence of full order observer of the system by using Lyapunov-like method and the linear matrix inequality (LMI) technique.A robust observer is designed for the system with disturbance.A sufficient condition is proposed for the existence of robust observer.Finally,an example is given to illustrate the effectiveness and feasibility of the proposed method in the paper.