Glaucoma infection is rapidly spreading globally and the number of glaucoma patients is expected to exceed 110 million by 2040. Early identification and detection of glaucoma is particularly important as it can easily lead to irreversible vision damage or even blindness if not treated with intervention in the early stages. Deep learning has attracted much attention in the field of computer vision and has been widely studied especially in the recognition and diagnosis of ophthalmic diseases. It is challenging to efficiently extract effective features for accurate grading of glaucoma in a limited dataset. Currently, in glaucoma recognition algorithms, 2D fundus images are mainly used to automatically identify the disease or not, but do not distinguish between early or late stages; however, in clinical practice, the treatment of early and late glaucoma is not the same, so it is more important to proceed to achieve accurate grading of glaucoma. This study uses a private dataset containing modal data, 2D fundus images, and 3D-OCT scanner images, to extract the effective features therein to achieve an accurate triple classification (normal, early, and moderately advanced) for optimal performance on various measures. In view of this, this paper proposes an automatic glaucoma classification method based on the attention mechanism and EfficientNetB3 network. The EfficientNetB3 network and ResNet34 network are built to extract and fuse 2D fundus images and 3D-OCT scanner images, respectively, to achieve accurate classification. The proposed auto-classification method minimizes feature redundancy while improving classification accuracy, and incorporates an attention mechanism in the two-branch model, which enables the convolutional neural network to focus its attention on the main features of the eye and discard the meaningless black background region in the image to improve the performance of the model. The auto-classification method combined with the cross-entropy function achieves the highest accuracy up to 97.83%. Since the proposed automatic grading method is effective and ensures reliable decision-making for glaucoma screening, it can be used as a second opinion tool by doctors, which can greatly reduce missed diagnosis and misdiagnosis by doctors, and buy more time for patient's treatment.