Glaucoma is the second-most-blinding eye disease in the world and accurate segmentation of the optic disc (OD) and optic cup (OC) is essential for the diagnosis of glaucoma. To solve the problems of poor real-time performance, high algorithm complexity, and large memory consumption of fundus segmentation algorithms, a lightweight segmentation algorithm, GlauNet, based on convolutional neural networks, is proposed. The algorithm designs an efficient feature-extraction network and proposes a multiscale boundary fusion (MBF) module, which greatly improves the segmentation efficiency of the algorithm while ensuring segmentation accuracy. Experiments show that the algorithm achieves Dice scores of 0.9701/0.8959, 0.9650/0.8621, and 0.9594/0.8795 on three publicly available datasets—Drishti-GS, RIM-ONE-r3, and REFUGE-train—for both the optic disc and the optic cup. The number of model parameters is only 0.8 M, and it only takes 13 ms to infer an 800 × 800 fundus image on a GTX 3070 GPU.