The paper proposes an edge-effect training multi-class fuzzy support vector machine (EFSVM). It treats the training data points with different importance in the training process, and especially emphasizes primary contribution of these points distributed in edge area of data sets for classification, and then assigns them greater fuzzy membership degrees, thus assures that the nearer these points are away from edge area of training sets and the greater their contribution are. At the same time EFSVM is systematically compared to two other fuzzy support vector machines and a Levenberg-Marquardt-based BP algorithm (LMBP). The classification results for both Iris data and remote sensing image show that EFSVM is the best and may effectively enhance pattern classification accuracy.