This paper presents an unsupervised Bayesian algorithm for hyperspectral image unmixing accounting for endmember variability. This variability is obtained by assuming that each pixel is a linear combination of random endmembers weighted by their corresponding abundances. An additive noise is also considered in the proposed model generalizing the normal compositional model. The proposed model is unsupervised since it estimates the abundances and both the mean and the covariance matrix of each endmember. A classification map indicating the class of each pixel is also obtained based on the estimated abundances. Simulations conducted on a real dataset show the potential of the proposed model in terms of unmixing performance for the analysis of hyperspectral images.