This paper studies a new Bayesian algorithm to unmix hyperspectral images. The algorithm is based on the recent normal compositional model introduced by Eismann. Contrary to the standard linear mixing model, the endmember spectra are assumed to be random signatures with know mean vectors. Appropriate prior distributions are assigned to the abundance coefficients to ensure the usual positivity and sum-to-one constraints. However, the resulting posterior distribution is too complex to obtain a closed form expression for the Bayesian estimators. A Markov chain Monte Carlo algorithm is then proposed to generate samples distributed according to the full posterior distribution. These samples are used to estimate the unknown model parameters. Several simulations are conducted on synthetic and real data to illustrate the performance of the proposed method.