Image classification is a challenging problem in computer vision. Its performance heavily depends on image features extracted and classifiers to be constructed. In this paper, we present a new support vector machine with mixture of kernels (SVM-MK) for image classification. On the one hand, the combined global and local block-based image features are extracted in order to reflect the intrinsic content of images as complete as possible. SVM-MK, on the other hand, is constructed to shoot for better classification performance. Experimental results on the Berg dataset show that the proposed image feature representation method together with the constructed image classifier, SVMMK, can achieve higher classification accuracy than conventional SVM with any single kernels as well as compare favorably with several state-of-the-art approaches.