Color fundus photography (CFP) and Optical coherence tomography (OCT) images are two of the most widely used modalities in the clinical diagnosis and management of retinal diseases. Despite the widespread use of multimodal imaging in clinical practice, few methods for automated diagnosis of eye diseases utilize correlated and complementary information from multiple modalities effectively. This paper explores how to leverage the information from CFP and OCT images to improve the automated diagnosis of retinal diseases. We propose a novel multimodal learning method, named geometric correspondence-based multimodal learning network (GeCoM-Net), to achieve the fusion of CFP and OCT images. Specifically, inspired by clinical observations, we consider the geometric correspondence between the OCT slice and the CFP region to learn the correlated features of the two modalities for robust fusion. Furthermore, we design a new feature selection strategy to extract discriminative OCT representations by automatically selecting the important feature maps from OCT slices. Unlike the existing multimodal learning methods, GeCoM-Net is the first method that formulates the geometric relationships between the OCT slice and the corresponding region of the CFP image explicitly for CFP and OCT fusion. Experiments have been conducted on a large-scale private dataset and a publicly available dataset to evaluate the effectiveness of GeCoM-Net for diagnosing diabetic macular edema (DME), impaired visual acuity (VA) and glaucoma. The empirical results show that our method outperforms the current state-of-the-art multimodal learning methods by improving the AUROC score 0.4%, 1.9% and 2.9% for DME, VA and glaucoma detection, respectively.