A recurrent neural network has been frequently used in equalizing the channel for fast communication systems. The existing techniques, however, have mainly dealt with time-invariant chamois. The modern environments of communication systems such as mobile ones have the time-varying feature due to fading. In this paper, powerful decision feedback - recurrent neural network is used as channel equalizer for nonlinear and time-varying system, and two kinds of algorithms, such as extended Kalman filter (EKF) and sigma-point Kalman filter (SPKF), are proposed; EKF is for fast convergence and good tracing function, and SPKF for overcoming the problems which can be developed during the process of first linearization for nonlinear system EKF.