In this paper, a method is presented for modelling a class of nonlinear systems which involves time-varying parameters. The system model proposed here is a type of nonlinear difference equation, where unknown parameters are assumed to be linearly involved in the system model. The principal line of attack is to assume that the nonlinear time varying function in the system can be expanded into the M known functions with unknown constant coefficients. First, the estimation process of unknown parameters is given by using the least squares method. Secondly, consistency properties and asymptotic normality conditions of the estimator are shown. Finally, two numerical examples are shown in order to demonstrate asymptotic properties of the estimator derived here.