Mammogram image is important for breast cancer screening, and typically obtained in a dual-view form, i.e., cranio-caudal (CC) and mediolateral oblique (MLO), to provide complementary information for clinical decisions. However, previous methods mostly learn features from the two views independently, which violates the clinical knowledge and ignores the importance of dual-view correlation in the feature learning. In this paper, we propose a dual-view correlation hybrid attention network (DCHA-Net) for robust holistic mammogram classification. Specifically, DCHA-Net is carefully designed to extract and reinvent deep feature maps for the two views, and meanwhile to maximize the underlying correlations between them. A hybrid attention module, consisting of local relation and non-local attention blocks, is proposed to alleviate the spatial misalignment of the paired views in the correlation maximization. A dual-view correlation loss is introduced to maximize the feature similarity between corresponding strip-like regions with equal distance to the chest wall, motivated by the fact that their features represent the same breast tissues, and thus should be highly-correlated with each other. Experimental results on the two public datasets, i.e., INbreast and CBIS-DDSM, demonstrate that the DCHA-Net can well preserve and maximize feature correlations across views, and thus outperforms previous state-of-the-art methods for classifying a whole mammogram as malignant or not.