This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomial functions leading to a polynomial post-nonlinear mixing model. A Bayesian algorithm and optimization methods are proposed to estimate the parameters involved in the model. The performance of the unmixing strategies is evaluated thanks to simulations conducted on synthetic and real data.