Recently, LSTSVM as a new binary SVM classifier based on nonparallel twin hyperplanes has shown a good classification performance, but the research on multi-class classification has still rarely been reported. In this paper, a multi-class LSTSVM classifier based on optimal directed acyclic graph is proposed. The idea of kernel parameter choice is used to realize the class separability criterion, an average distance measure and a non-repetitive sequence number rearrangement method are offered in order to reduce the cumulative errors caused by DAG structure. The experimental results on UCI datasets show that the proposed ODAG-LSTSVM algorithm has better classification accuracy and considerably lesser computational time.