A new kernel-based learning algorithm called kernel affine subspace nearest point (KASNP) approach is proposed in this paper. Inspired by the geometrical explanation of support vector machines (SVMs) and its nearest point problem in convex hulls, we extend the convex hull of each class to its corresponding affine subspace in high dimensional space induced by kernel. In two class affine subspaces, KASNP finds the nearest points and then constructs a separating hyperplane, which bisects the line segment joining them. The nearest point problem of KASNP is only an unconstrained optimal problem whose solution can be directly computed. Compared with SVM, KASNP avoids solving convex quadratic programming. Experiments on two-spiral dataset, two UCI credit datasets, and face recognition datasets show that our proposed KASNP is effective for data classification.