Meaning Representation (AMR) parsing aims to translate sentences to semantic representation with a hierarchical structure, and is recently empowered by pretrained sequenceto-sequence models. However, there exists a gap between their flat training objective (i.e., equally treats all output tokens) and the hierarchical AMR structure, which limits the model generalization. To bridge this gap, we propose a Hierarchical Curriculum Learning (HCL) framework with Structure-level (SC) and Instance-level Curricula (IC). SC switches progressively from core to detail AMR semantic elements while IC transits from structuresimple to -complex AMR instances during training. Through these two warming-up processes, HCL reduces the difficulty of learning complex structures, thus the flat model can better adapt to the AMR hierarchy. Extensive experiments on AMR2.0, AMR3.0, structurecomplex and out-of-distribution situations verify the effectiveness of HCL. * Equal Contribution.