This paper studies a generalized bilinear model and a hierarchical Bayesian algorithm for unmixing hyperspectral images. The proposed model is a generalization of the accepted linear mixing model but also of a bilinear model recently introduced in the literature. Appropriate priors are chosen for its parameters in particular to satisfy the positivity and sum-to-one constraints for the abundances. The joint posterior distribution of the unknown parameter vector is then derived. A Metropolis-within-Gibbs algorithm is proposed which allows samples distributed according to the posterior of interest to be generated and to estimate the unknown model parameters. The performance of the resulting unmixing strategy is evaluated via simulations conducted on synthetic and real data.