Glaucoma is an ophthalmic disease related to damage in the optic nerve and it is without symptoms in its early stages. Left untreated, it can lead to vision limitation and blindness. Eye fundus images have been widely accepted by medical personnel to examine the morphology and texture of the optic nerve head and the physiologic cup but glaucoma diagnosis is still subjective and without clear consensus among experts. This paper presents a multi-stage deep learning model for glaucoma diagnosis based on a curriculum learning strategy. In curriculum learning, a model is sequentially trained to solve incrementally difficult tasks. Our proposed model includes the following stages: segmentation of the optic disc and physiological cup, prediction of morphometric features from segmentations, and prediction of disease level (healthy, suspicious and glaucoma). The experimental evaluation shows that our proposed method outperforms conventional convolutional deep learning models from the state of the art reported on the RIM-ONE-v1 and DRISHTI-GS1 datasets with an accuracy of 89.4% and an AUC of 0.82 respectively.