Shared-account Cross-domain Sequential Recommendation (SCSR) is the task of recommending the next item based on a sequence of recorded user behaviors, where multiple users share a single account, and their behaviours are available in multiple domains. Existing work on solving SCSR mainly relies on mining sequential patterns via RNN-based models, which are not expressive enough to capture the relationships among multiple entities. Moreover, all existing algorithms try to bridge two domains via knowledge transfer in the latent space, and the explicit cross-domain graph structure is unexploited. In this work, we propose a novel graph-based solution, namely DA-GCN, to address the above challenges. Specifically, we first link users and items in each domain as a graph. Then, we devise a domain-aware graph convolution network to learn user-specific node representations. To fully account for users' domain-specific preferences on items, two novel attention mechanisms are further developed to selectively guide the message passing process. Extensive experiments on two real-world datasets are conducted to demonstrate the superiority of our DA-GCN method.