A variation of RBF (radial basis function) classifier based on supervised (or adaptively) ceneter selection and weighted norm is formulated and then tested in labeling overlapped data sets generated from two binormal distributions in this paper. Besides its simplicity, the experimental results and the comparsions to other classifiers suggest that this method is significant in capability owing to offering reasonable classifications with mild computation costs. Moreover, this variation outperforms the RBF based on exact interpolation not just in accuracy but in efficiency as well.