In this paper, a finite–series expansion method is presented for the analysis and parameter identification of a discrete non-linear system that is described by a Hammerstein model consisting of a memoryless gain of polynomial form followed by a linear discrete system. By expanding the system variables in discrete Legendre orthogonal polynomials (DLOPs) and using the shift and product operational properties of DLOPs, the Hammerstein model is converted into a set of linear equations in the DLOP coefficients of unknown output variables and in the system parameters. This converted set of linear algebraic equations is convenient for finding the DLOP coefficients of unknown variables. Also, it allows one to determine the unknown system parameters using the least-squares method when the system input and output data are available.