Canonical correlation analysis (CCA) is a classical yet powerful tool for learning two-view feature representation in various fields. But, most CCA approaches are based on the conventional covariance measure, which makes them difficult to uncover the complicatedly nonlinear relationship between distinct features. In this paper, we address the preceding problem and propose two novel CCA approaches in a supervised manner by using a general covariance metric. The proposed approaches not only consider the label information of training data, but also the nonlinear relationship between different features rather than samples, which leads to greater flexibility in many practical applications. A series of experimental results on five benchmark datasets demonstrate the effectiveness of our proposed methods in terms of classification accuracy.