Hierarchical Text Classification (HTC), which aims to predict text labels organized in hierarchical space, is a significant task lacking in investigation in natural language processing. Existing methods usually encode the entire hierarchical structure and fail to construct a robust label-dependent model, making it hard to make accurate predictions on sparse lower-level labels and achieving low Macro-F1. In this paper, we explore the level dependency and path dependency of the label hierarchy in a generative way for building the knowledge of upper-level labels of current path into lower-level ones, and thus propose a novel PAAM-HiA-T5 model for HTC: a hierarchy-aware T5 model with path-adaptive attention mechanism. Specifically, we generate a multi-level sequential label structure to exploit hierarchical dependency across different levels with Breadth-First Search (BFS) and T5 model. To further improve label dependency prediction within each path, we then propose an original path-adaptive attention mechanism (PAAM) to lead the model to adaptively focus on the path where the currently generated label is located, shielding the noise from other paths. Comprehensive experiments on three benchmark datasets show that PAAM-HiA-T5 greatly outperforms all state-of-the-art HTC approaches especially in Macro-F1.