A method which we call support vector machine with graded resolution (SVM-GR) is proposed in this paper. During the training of the SVM-GR, we first form data granules to train the SVM-GR and remove those data granules that are not support vectors. We then use the remaining training samples to train the SVM-GR. Compared with the traditional SVM, our SVM-GR algorithm requires fewer training samples and support vectors, hence the computational time and memory requirements for the SVM-GR are much smaller than those of a conventional SVM that use the entire dataset. Experiments on benchmark data sets show that the generalization performance of the SVM-GR is comparable to the traditional SVM.