Primary open-angle glaucoma (POAG) is one of the leading causes of irreversible blindness in the United States and worldwide. POAG prediction before onset plays an important role in early treatment. Although deep learning methods have been proposed to predict POAG, these methods mainly focus on current status prediction. In addition, all these methods used a single image as input. On the other hand, glaucoma specialists determine a glaucomatous eye by comparing the follow-up optic nerve image with the baseline along with supplementary clinical data. To simulate this process, we proposed a Multi-scale Multi-structure Siamese Network (MMSNet) to predict future POAG event from fundus photographs. The MMSNet consists of two side-outputs for deep supervision and 2D blocks to utilize two-dimensional features to assist classification. The MMSNet network was trained and evaluated on a large dataset: 37,339 fundus photographs from 1,636 Ocular Hypertension Treatment Study (OHTS) participants. Extensive experiments show that MMSNet outperforms the state-of-the-art on two “POAG prediction before onset” tasks. Our AUC are 0.9312 and 0.9507, which are 0.2204 and 0.1490 higher than the state-of-the-art, respectively. In addition, an ablation study is performed to check the contribution of different components. These results highlight the potential of deep learning to assist and enhance the prediction of future POAG event. The proposed network will be publicly available on https://github.com/bionlplab/MMSNet.