Abstract: In this paper, the notion of ``scaled convex hull (SCH)'' is employed and a set of theoretical results are exploited to support it, through which the nonseparable support vector machine (SVM) classification problems can be transformed to the problems of computing the pair of nearest points between SCHs. As a practical application of the SCH framework, a popular nearest point algorithm has been adopted to find the pair of nearest points between SCHs (each is generated by training patterns of each class), and the separating hyperplane bisects, and is normal to the line segment joining these two nearest points. Then, the proposed method is generalied to solve nonlinear problems and a simplified version for the nonlinear case is presented. The theoretical analysis and experiments show that the proposed method may achieve better performance than the state-of-the-art methods in terms of the kernel evaluations and execution time, making it suitable for large scale classification.