Fine-grained hashing is a new topic in the field of hashing-based retrieval and has not been well explored up to now. In this paper, we raise three key issues that fine-grained hashing should address simultaneously, i.e., fine-grained feature extraction, feature refinement as well as a well-designed loss function. In order to address these issues, we propose a novel Fine-graIned haSHing method with a double-filtering mechanism and a proxy-based loss function, FISH for short. Specifically, the double-filtering mechanism consists of two modules, i.e., Space Filtering module and Feature Filtering module, which address the fine-grained feature extraction and feature refinement issues, respectively. Thereinto, the Space Filtering module is designed to highlight the critical regions in images and help the model to capture more subtle and discriminative details; the Feature Filtering module is the key of FISH and aims to further refine extracted features by supervised re- weighting and enhancing. Moreover, the proxy-based loss is adopted to train the model by preserving similarity relationships between data instances and proxy-vectors of each class rather than other data instances, further making FISH much efficient and effective. Experimental results demonstrate that FISH achieves much better retrieval performance compared with state-of-the-art fine-grained hashing methods, and converges very fast. The source code is publicly available: https://github.com/chenzhenduo/FISH.