This paper concerned with the design method of state and disturbance observers for discrete-time nonlinear systems. An augmented model is constructed by assuming that the estimated disturbance is in state-space variable form. A sufficient condition for the existence and convergence of the robust observer is proposed in terms of linear matrix inequality (LMI). The gains of the state and disturbance observers are obtained via solving the LMI. Finally, a numerical example is given to show the effectiveness of the proposed method.