To demonstrate the identification of corneal diseases using a novel deep learning algorithm. A novel hierarchical deep learning network, which is composed of a family of multi-task multi-label learning classifiers representing different levels of eye diseases derived from a predefined hierarchical eye disease taxonomy was designed. Next, we proposed a multi-level eye disease-guided loss function to learn the fine-grained variability of eye diseases features. The proposed algorithm was trained end-to-end directly using 5,325 ocular surface images from a retrospective dataset. Finally, the algorithm's performance was tested against 10 ophthalmologists in a prospective clinic-based dataset with 510 outpatients newly enrolled with diseases of infectious keratitis, non-infectious keratitis, corneal dystrophy or degeneration, and corneal neoplasm. The area under the ROC curve of the algorithm for each corneal disease type was over 0.910 and in general it had sensitivity and specificity similar to or better than the average values of all ophthalmologists. Confusion matrices revealed similarities in misclassification between human experts and the algorithm. In addition, our algorithm outperformed over all four previous reported methods in identified corneal diseases. The proposed algorithm may be useful for computer-assisted corneal disease diagnosis.