A model following control system (MFCS) can output general signals following the desired ones. In this paper, a method of nonlinear MFCS will be extended to be a nonlinear descriptor system in discrete time. The nonlinear system studied in this paper has the property of norm constraint $||f(v(k))||\leq\alpha+\beta||v(k)||^\gamma$, where $\alpha\ge0$, $\beta\ge0$ , $0\leq\gamma<1$. In this case, a new criterion is proposed to ensure the internal states be stable.