In this paper, we propose a new method aiming at reducing the noise in hyperspectral images. It is based on the nonlinear generalization of Principal Component Analysis (NLPCA). The NLPCA is performed by an auto associative neural network that have the hyperspectral image as input and is trained to reconstruct the same image at the output. Thanks to its bottleneck structure, the AANN forces the hyper spectral image to be projected in a lower dimensionality feature space where noise as well as both linear and nonlinear correlations between spectral bands are removed. This process permits to obtain enhancements in terms of hyperspectral image quality. Experiments are conducted on different real hyper spectral images, with different contexts and resolutions. The results are qualitatively and quantitatively discussed and demonstrate the interest of the proposed method as compared to traditional approaches.