This paper proposes a novel approach to classify hyperspectral (HS) images using both spectral and spatial information. It first consists of a supervised spectral dimension reduction step that transforms the HS image into a score image that has fewer channels. These channels are chosen so as to enhance distances between classes to be discriminated and to reduce background variability, thus leading to edges that correspond to actual class borders. In the second step, applying an edge-preserving spatial regularization on this score image leads to a lowered background variability. Therefore, in the third step, the pixel-wise classification of the regularized score image is greatly improved. We implement this approach using the partial least squares (PLS) method for spectral dimension reduction and the anisotropic diffusion for spatial regularization. We then compare linear discriminant analysis (LDA), K-nearest neighbors (KNN), and support vector machine (SVM) for the class decision. The effectiveness of our method was evaluated with three remotely sensed HS images. Its robustness was also assessed for different training sets, since the latter has a crucial influence on classification performance. On average, our method gave better results in terms of classification accuracy and was more robust than other classification methods tested with the same images.