•A Kautz-basis-expansion based Hammerstein system identification method is proposed.•Separable least squares is adopted to estimate linear and nonlinear parameters.•Best linear approximation is presented to choose initial values of pole parameters.•LM algorithm is presented for the optimization of pole and nonlinear parameters. This paper proposes a novel Hammerstein system identification method based on the Kautz basis expansion and the separable least squares method. In this method, to reduce the parameters to be identified, the impulse response function (IRF) of the linear subsystem is expanded by orthogonal Kautz functions, the pole parameters among which should be optimized. In addition, to improve the condition number of matrix during the identification process, the separable least squares optimization method is adopted to estimate the linear and nonlinear parameters. The separable least squares approach can simultaneously estimate the linear and nonlinear parameters in a least squares framework. Furthermore, based on the best linear approximation, an effective method for the choice of initial values of pole parameters is presented, and based on the back propagation through-time technique and the Levenberg-Marquardt algorithm, an optimization algorithm for pole and nonlinear parameters is presented in this paper. The simulation studies verify the effectiveness of the proposed Hammerstein system identification method.