Classical linear discriminant analysis (LDA) (Fisher, 1936) implicitly assumes the classification boundary depends on only one linear combination of the predictors. This restriction can lead to poor classification in applications where the decision boundary depends on multiple linear combinations of the predictors. To overcome this challenge, we first project the predictors onto an envelope central space and then perform LDA based on the sufficient predictor. The performance of the proposed method in improving classification accuracy is demonstrated in both synthetic data and real applications.