In this paper, a space partition method called “Label Constrained Graph Partition” (LCGP) is presented to solve the Sample-InterweavingPhenomenon in the original space. We first divide the entire training set into subclasses by means of LCGP, so that the scopes of subclasses will not overlap in the original space. Then “Most Discriminant Subclass Distribution” (MDSD) criterion is proposed to decide the best partition result. At last, typical LDA algorithm is applied to obtain the feature space and the RBF neural network classifier is utilized to make the final decision. The computer simulations and comparisons are given to demonstrate the performance of our method.