Hierarchical multi-granularity image classification is a challenging task that aims to tag each given image with multiple granularity labels simultaneously. Existing methods tend to overlook that different image regions contribute differently to label prediction at different granularities, and also insufficiently consider relationships between the hierarchical multi-granularity labels. We introduce a sequence-to-sequence mechanism to overcome these two problems and propose a multi-granularity sequence generation (MGSG) approach for the hierarchical multi-granularity image classification task. Specifically, we introduce a transformer architecture to encode the image into visual representation sequences. Next, we traverse the taxonomic tree and organize the multi-granularity labels into sequences, and vectorize them and add positional information. The proposed multi-granularity sequence generation method builds a decoder that takes visual representation sequences and semantic label embedding as inputs, and outputs the predicted multi-granularity label sequence. The decoder models dependencies and correlations between multi-granularity labels through a masked multi-head self-attention mechanism, and relates visual information to the semantic label information through a cross-modality attention mechanism. In this way, the proposed method preserves the relationships between labels at different granularity levels and takes into account the influence of different image regions on labels with different granularities. Evaluations on six public benchmarks qualitatively and quantitatively demonstrate the advantages of the proposed method. Our project is available at https://github.com/liuxindazz/mgsg.