With the popularization of computer-aided diagnosis (CAD) technologies, more and more deep learning methods are developed to facilitate the detection of ophthalmic diseases. In this article, the deep learning-based detections for some common eye diseases, including cataract, glaucoma, and age-related macular degeneration (AMD), are analyzed. Generally speaking, morphological change in retina reveals the presence of eye disease. Then, while using some existing deep learning methods to achieve this analysis task, the satisfactory performance may not be given, since fundus images usually suffer from the impact from data imbalance and outliers. It is, therefore, expected that with the exploration of effective and robust deep learning algorithms, the detection performance could be further improved. Here, we propose a deep learning model combined with a novel mixture loss function to automatically detect eye diseases, through the analysis of retinal fundus color images. Specifically, given the good generalization and robustness of focal loss and correntropy-induced loss functions in addressing complex dataset with class imbalance and outliers, we present a mixture of those two losses in deep neural network model to improve the recognition performance of classifier for biomedical data. The proposed model is evaluated on a real-life ophthalmic dataset. Meanwhile, the performance of deep learning model with our proposed loss function is compared with the baseline models, while adopting accuracy, sensitivity, specificity, Kappa, and area under the receiver operating characteristic curve (AUC) as the evaluation metrics. The experimental results verify the effectiveness and robustness of the proposed algorithm.