Abstract Representing high-volume and high-order data is an essential problem, especially in machine learning field. Although existing two-dimensional (2D) discriminant analysis achieves promising performance, the single and linear projection features make it difficult to analyze more complex data. In this paper, we propose a novel convolutional two-dimensional linear discriminant analysis (2D LDA) method for data representation. In order to deal with nonlinear data, a specially designed Convolutional Neural Networks (CNN) is presented, which can be proved having the equivalent objective function with common 2D LDA. In this way, the discriminant ability can benefit from not only the nonlinearity of Convolutional Neural Networks, but also the powerful learning process. Experiment results on several datasets show that the proposed method performs better than other state-of-the-art methods in terms of classification accuracy.