Multi-Label Image Classification (MLIC) aims to predict a set of labels that present in an image. The key to deal with such problem is to mine the associations between image contents and labels, and further obtain the correct assignments between images and their labels. In this paper, we treat each image as a bag of instances, and reformulate the task of MLIC as a instance-label matching selection problem. To model such problem, we propose a novel deep learning framework named Graph Matching based Multi-Label Image Classification (GM-MLIC), where Graph Matching (GM) scheme is introduced owing to its excellent capability of excavating the instance and label relationship. Specifically, we first construct an instance spatial graph and a label semantic graph respectively, and then incorporate them into a constructed assignment graph by connecting each instance to all labels. Subsequently, the graph network block is adopted to aggregate and update all nodes and edges state on the assignment graph to form structured representations for each instance and label. Our network finally derives a prediction score for each instance-label correspondence and optimizes such correspondence with a weighted cross-entropy loss. Extensive experiments conducted on various datasets demonstrate the superiority of our proposed method.