With the development of remote sensing technology and imaging spectrometer ,the resolution of hyperspectral remote sensing image has been continually improved,its vast amount of data not only improves the ability of the remote sensing detection but also brings great difficulties for analyzing and processing at the same time.Band selection of hyperspectral imagery can effectively reduce data redundancy and improve classification accuracy and efficiency.So how to select the optimum band combination from hundreds of bands of hyperspectral images is a key issue.In order to solve these problems,we use spectral clustering algorithm based on graph theory.Firstly,taking of the original hyperspectral image bands as data points to be clustered ,mutual information between every two bands is calculated to generate the similarity matrix.Then according to the graph partition theory,spectral decomposition of the non-normalized Laplacian matrix generated by the similarity matrix is used to get the clusters,which the similarity between is small and the similarity within is large.In order to achieve the purpose of dimensionality reduction,the inter-class separability factor of feature types on each band is calculated,which is as the reference index to choose the representative bands in the clusters furthermore.Finally,the support vector machine and minimum distance classification methods are employed to classify the hyperspectral image after band selection.The method in this paper is different from the traditional unsupervised clustering method,we employ spectral clustering algorithm based on graph theory and compute the inter-class separability factor based on a priori knowledge to select bands.Comparing with traditional adaptive band selection algorithm and band index based on automatically subspace divided algorithm,the two sets of experiments results show that the overall accuracy of SVM is about 94.08% and 94.24% and the overall accuracy of MDC is about 87.98% and 89.09%,when the band selection achieves a relatively optimal number of clusters using the method propoesd in this paper .It effectively remains spectral information and improves the classification accuracy.