An accurate and automated tissue segmentation algorithm for retinal optical coherence tomography (OCT) images is crucial for the diagnosis of glaucoma. However, due to the presence of the optic disc, the anatomical structure of the peripapillary region of the retina is complicated and is challenging for segmentation. To address this issue, we develop a novel graph convolutional network (GCN)-assisted two-stage framework to simultaneously label the nine retinal layers and the optic disc. Specifically, a multi-scale global reasoning module is inserted between the encoder and decoder of a U-shape neural network to exploit anatomical prior knowledge and perform spatial reasoning. We conduct experiments on human peripapillary retinal OCT images. We also provide public access to the collected dataset, which might contribute to the research in the field of biomedical image processing. The Dice score of the proposed segmentation network is 0.820 ± 0.001 and the pixel accuracy is 0.830 ± 0.002, both of which outperform those from other state-of-the-art techniques.