Computer-aided diagnosis of retinopathy is a hot research topic in the field of medical image classification, where optical coherence tomography (OCT) is an important basis for the diagnosis of ophthalmic diseases. Traditional approaches to multi-label image classification learn independent classifiers for each category and employ ranking or thresholding on the classification results. These techniques, although working well, fail to explicitly exploit the label dependencies in an image. In this paper, two publicly available retinal OCT image datasets are integrated and screened. Then, an end-to-end deep learning algorithmic framework based on CNN-RNN Unified Neural Networks was proposed to automatically and reliably classify six categories of retinal OCT images. Numerical results suggest that the proposed algorithm works well in terms of accuracy, precision, sensitivity and specificity, approaching or even partially surpassing the performance of clinical experts. It is valuable in promoting computer-aided diagnosis towards practical clinical applications and improving the efficiency of clinical diagnosis of retinal diseases.