This paper studies a new unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of endmembers which are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, endmembers are modeled as Gaussian vectors with known means (resulting from an endmember extraction algorithm such as the famous N-FINDR or VCA algorithm). This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas a conjugate prior is chosen for the variance. The computational complexity of the resulting Bayesian estimators is alleviated by constructing an hybrid Gibbs algorithm to generate abundance and variance samples distributed according to the posterior distribution of the unknown parameters. The associated hyperparameter is also generated. The performance of the proposed methodology is evaluated thanks to simulation results conducted on synthetic and real images.