Glaucoma is one of the ophthalmic diseases that may cause blindness, for which early detection and treatment are very important. Fundus images and optical coherence tomography (OCT) images are both widely-used modalities in diagnosing glaucoma. However, existing glaucoma grading approaches mainly utilize a single modality, ignoring the complementary information between fundus and OCT. In this paper, we propose an efficient multi-modality supervised contrastive learning framework, named COROLLA, for glaucoma grading. Through layer segmentation as well as thickness calculation and projection, retinal thickness maps are extracted from the original OCT volumes and used as a replacing modality, resulting in more efficient calculations with less memory usage. Given the high structure and distribution similarities across medical image samples, we employ supervised contrastive learning to increase our models' discriminative power with better convergence. Moreover, feature-level fusion of paired fundus image and thickness map is conducted for enhanced diagnosis accuracy. On the GAMMA dataset, our COROLLA framework achieves overwhelming glaucoma grading performance compared to state-of-the-art methods.