A nonlinear parsimonious feature selection algorithm is presented in this paper. It is based on a Gaussian mixture model (GMM). GMM are used for classifying hyperspectral images. The algorithm selects iteratively spectral features that maximizes an estimate of the correct classification rate. In order to perform fast in terms of computing time, an efficient implementation is proposed. First, the GMM can be updated when the estimation of the correct classification rate is computed, rather re-estimate the full model. Secondly, using marginalization of the GMM, sub models can be directly obtain from the full model learns with all the spectral features. Experimental results for three hyperspectral data sets show that the method performs very well and is able to extract very few spectral channels.