Graph data, as a kind of widely-existing data in the real world, naturally represent complex interactions between elements of composite objects. The classification of graph data is a very important and extremely challenging research topic. There are many key applications in the fields of bio/chemical informatics, such as molecular attribute classification and drug discovery. However, there still lacks a comprehensive review of research on graph classification. This survey first formulates the problem of graph classification and describes the main challenges of this problem; then this survey categorizes graph classification methods into similarity-based methods and graph neural network based methods. Moreover, evaluation metrics for graph classification, benchmark datasets, and comparison results are given. Finally, the application scenarios of graph classifications are summarized, and the research trends of graph classification are also discussed.