This paper proposes to combine standard SVM classification with a hierarchical approach to increase SVM classification accuracy as well as reduce computational load of SVM testing. Support vectors are obtained by applying SVM training to the entire original training data. For classification, multi-level two-dimensional wavelet decomposition is applied to each hyperspectral image band and low spatial frequency components of each level are used for hierarchical classification. Initially, conventional SVM classification is carried out in the highest hierarchical level (lowest resolution) using all support vectors and a one-to-one multiclass classification strategy, so that all pixels in the lowest resolution are classified. In the sub-sequent levels (higher resolutions) pixels are classified using the class information of the corresponding neighbor pixels of the upper level. Therefore, the classification at a lower level is carried out using only the support vectors of classes to which corresponding neighbor pixels in the higher level are assigned to. Because classification with all support vectors is only utilized at the lowest resolution and classification of higher resolutions requires a subset of the support vectors, this approach reduces the overall computational load of SVM classification and provides reduced SVM testing time compared to standard SVM. Furthermore, the proposed approach provides significantly better classification accuracy as it exploits spatial correlation thanks to hierarchical processing.