Most of the aspect based sentiment analysis research aims at identifying the sentiment polarities toward some explicit aspect terms while ignores implicit aspects in text. To capture both explicit and implicit aspects, we focus on aspect-category based sentiment analysis, which involves joint aspect category detection and category-oriented sentiment classification. However, currently only a few simple studies have focused on this problem. The shortcomings in the way they defined the task make their approaches difficult to effectively learn the inner-relations between categories and the inter-relations between categories and sentiments. In this work, we re-formalize the task as a category-sentiment hierarchy prediction problem, which contains a hierarchy output structure to first identify multiple aspect categories in a piece of text, and then predict the sentiment for each of the identified categories. Specifically, we propose a Hierarchical Graph Convolutional Network (Hier-GCN), where a lower-level GCN is to model the inner-relations among multiple categories, and the higher-level GCN is to capture the inter-relations between aspect categories and sentiments. Extensive evaluations demonstrate that our hierarchy output structure is superior over existing ones, and the Hier-GCN model can consistently achieve the best results on four benchmarks.