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Glaucoma is one of the three leading causes of blindness in the world and is predicted to affect around 80 million people by 2020. The optic cup (OC) to optic disc (OD) ratio (CDR) in fundus images plays a pivotal role in the screening and diagnosis of glaucoma. Existing methods usually crop the optic disc region first, and subsequently perform segmentation in this region. However, these approaches come up with high complexities due to the separate operations. To remedy this issue, we propose a Region Focus Network (RF-Net) that innovatively integrates detection and multi-class segmentation into a unified architecture for end-to-end joint optic disc and cup segmentation with global optimization. The key idea of our method is designing a novel multi-class mask branch which generates a high-quality segmentation in the detected region for both disc and cup. To bridge the connection between the backbone and multi-class mask branch, a Fusion Feature Pooling (FFP) structure is presented to extract features from each level of the pyramid network and fuse them into a final feature representation for segmentation. Extensive experimental results on the REFUGE-2018 challenge dataset and the Drishti-GS dataset show that the proposed method achieves the best performance, compared with competitive approaches reported in the literature and the official leaderboard. Our code will be released soon.