Retinopathy of prematurity (ROP) is one of the main eye diseases that cause blindness in children. Discovering and treating early stages 1–3 of ROP prevent the disease from progressing. This paper explores the automatic classification and diagnosis of stages 0–3 of ROP using deep convolutional neural networks. The performance of the classifier is gradually improved through a variety of experimental strategies such as training models (VGG19 and Resnet18), transfer learning of pre-trained models (InceptionV3, XceptionV3 and Inception_Resnet), and ensemble learning. In particular, the introduction of a weighted ensemble strategy successfully improves the technical problem that stages 1&2 of ROP are difficult to distinguish, which is generally believed by scholars. Finally, in the experiment, the weighted ensemble classifier achieved the best classification performance for the early stages of ROP, the accuracy and sensitivity were 96.03% and 94.90%, respectively.