Glaucoma is one of the leading causes of irreversible vision loss. Many approaches have recently been proposed for automatic glaucoma detection based on fundus images. However, none of the existing approaches can efficiently remove high redundancy in fundus images for glaucoma detection, which may reduce the reliability and accuracy of glaucoma detection. To avoid this disadvantage, this paper proposes an attention-based convolutional neural network (CNN) for glaucoma detection, called AG-CNN. Specifically, we first establish a large-scale attention-based glaucoma (LAG) database, which includes 11 760 fundus images labeled as either positive glaucoma (4878) or negative glaucoma (6882). Among the 11 760 fundus images, the attention maps of 5824 images are further obtained from ophthalmologists through a simulated eye-tracking experiment. Then, a new structure of AG-CNN is designed, including an attention prediction subnet, a pathological area localization subnet, and a glaucoma classification subnet. The attention maps are predicted in the attention prediction subnet to highlight the salient regions for glaucoma detection, under a weakly supervised training manner. In contrast to other attention-based CNN methods, the features are also visualized as the localized pathological area, which are further added in our AG-CNN structure to enhance the glaucoma detection performance. Finally, the experiment results from testing over our LAG database and another public glaucoma database show that the proposed AG-CNN approach significantly advances the state-of-the-art in glaucoma detection.