Canonical correlation analysis (CCA) is an effective way to find two appropriate subspaces in which Pearson's correlation coefficients are maximized between projected random vectors. Due to its well-established theoretical support and relatively efficient computation, CCA is widely used as a joint dimension reduction tool and has been successfully applied to many image processing and computer vision tasks. However, as reported, the traditional CCA suffers from overfitting in many practical cases. In this paper, we propose sufficient CCA (S-CCA) to relieve CCA's overfitting problem, which is inspired by the theory of sufficient dimension reduction. The effectiveness of S-CCA is verified both theoretically and experimentally. Experimental results also demonstrate that our S-CCA outperforms some of CCA's popular extensions during the prediction phase, especially when severe overfitting occurs.