Given a database schema, Text-to-SQL aims to translate a natural language question into the corresponding SQL query. Under the setup of cross-domain, traditional semantic parsing models struggle to adapt to unseen database schemas. To improve the model generalization capability for rare and unseen schemas, we propose a new architecture, ShadowGNN, which processes schemas at abstract and semantic levels. By ignoring names of semantic items in databases, abstract schemas are exploited in a well-designed graph projection neural network to obtain delexicalized representation of question and schema. Based on the domain-independent representations, a relation-aware transformer is utilized to further extract logical linking between question and schema. Finally, a SQL decoder with context-free grammar is applied. On the challenging Text-to-SQL benchmark Spider, empirical results show that ShadowGNN outperforms state-of-the-art models. When the annotated data is extremely limited (only 10% training set), ShadowGNN gets over absolute 5% performance gain, which shows its powerful generalization ability. Our implementation will be open-sourced at https://github. com/WowCZ/shadowgnn.