Hyperspectral image (HSI) recovery, as an upstream image processing task, holds significant importance for downstream tasks such as classification, segmentation, and detection. In recent years, HSI recovery methods based on non-local prior representations have demonstrated outstanding performance. However, these methods employ a fixed-format factor to represent the non-local self-similarity tensor groups, making them unable to adapt to diverse missing scenarios. To address this issue, we introduce the concept of granularity in tensor decomposition for the first time and propose an HSI recovery model constrained by multi-granularity non-local self-similarity priors. Specifically, the proposed model alternately performs coarse-grained decomposition and fine-grained decomposition on the non-local self-similarity tensor groups. Among them, the coarse-grained decomposition builds upon Tucker tensor decomposition, which extracts global structural information of the image by performing singular value shrinkage on the mode-unfolded matrices. The fine-grained decomposition employs the FCTN decomposition, capturing local detail information through modeling pairwise correlations among factor tensors. This architectural approach achieves a unified representation of global, local, and non-local priors for HSIs. Experimental results demonstrate that the model has strong applicability and exhibits outstanding recovery effects in various types of missing scenes such as pixels and stripes.