For hyperspectral image classification, a Support Vector Machine (SVM) algorithm with composite kernels was presented to fuse both the spectral information and spatial information of the image. The algorithm adopts Principal Component Analysis (PCA) algorithm to extract the image feature and reduce the dimension for hyperspectral image,and uses the Virtual Dimension (VD) algorithm to estimate the Intrinsic Dimension (ID) of the image. Then, the remained number of Principal Components (PCs) was determined on the basis of the ID.Furthermore, spatial features were extracted by mathematical morphology from the remained PCs,and the Extended Morphological Profile (EMP) vector of image was obtained. By combination of different strategies to construct composite kernels, the spatial information was introduced into the classifier to implement the classification with the SVM and based on both the spectral information and spatial information. Hyperspectral image experiments indicate that the overall accuracy and Kappa coefficients of the proposed approach increase about 2% without increasing the training time obviously. Compared with the classifiers only using the spatial or spectral information, the proposed method shows a lot advantages.