Abstract Robust 3D mesh watermarking is a traditional research topic in computer graphics, which provides an efficient solution to the copyright protection for 3D meshes. Traditionally, researchers need manually design watermarking algorithms to achieve sufficient robustness for the actual application scenarios. In this paper, we propose the first deep learning-based 3D mesh watermarking network, which can provide a more general framework for this problem. In detail, we propose an end-to-end network, consisting of a watermark embedding sub-network, a watermark extracting sub-network and attack layers. We employ the topology-agnostic graph convolutional network (GCN) as the basic convolution operation, therefore our network is not limited by registered meshes (which share a fixed topology). For the specific application scenario, we can integrate the corresponding attack layers to guarantee adaptive robustness against possible attacks. To ensure the visual quality of watermarked 3D meshes, we design the curvature consistency loss function to constrain the local geometry smoothness of watermarked meshes. Experimental results show that the proposed method can achieve more universal robustness while guaranteeing comparable visual quality.