Abstract: In this paper we first prove that the optimal discriminant direction of Maximum scatter difference (MSD) discriminant criterion with a certain value c0 is equivalent to the optimal Fisher discriminant direction. Second, sample recognition rate curves of MSD are illustrated. The recognition rate curve is usually a pulse curve when the within-class scatter matrix is nonsingular. With the increase of parameter C, the recognition rate of MSD also increases. The recognition rate of MSD achieves its maximum when C is equal to c0. In addition, former study showed that, when the within-class scatter matrix is singular, MSD criterion is approaching the large margin linear projection criterion as parameter C increases.Moreover, the recognition rate curve of MSD is non-decreasing. Thus, an adaptive classification algorithm based on maximum scatter difference discriminant criterion is proposed based on these facts. The new algorithm can tune parameter C automatically according to the characteristics of training samples. Experiment conducted on 6 datasets from UCI Machine Learning Repository and AR face database demonstrates that the adaptive classification algorithm for maximum scatter difference has good classification property.