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Understanding what online users may pay attention to is key to content recommendation and search services. These services will benefit from a highly structured and web-scale ontology of entities, concepts, events, topics and categories. While existing knowledge bases and taxonomies embody a large volume of entities and categories, we argue that they fail to discover properly grained concepts, events and topics in the language style of online population. Neither is a logically structured ontology maintained among these notions. In this paper, we present GIANT, a mechanism to construct a user-centered, web-scale, structured ontology, containing a large number of natural language phrases conforming to user attentions at various granularities, mined from a vast volume of web documents and search click graphs. Various types of edges are also constructed to maintain a hierarchy in the ontology. We present our graph-neural-network-based techniques used in GIANT, and evaluate the proposed methods as compared to a variety of baselines. GIANT has produced the Attention Ontology, which has been deployed in various Tencent applications involving over a billion users. Online A/B testing performed on Tencent QQ Browser shows that Attention Ontology can significantly improve click-through rates in news recommendation.