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Text-to-image person re-identification (ReID) aims to search for pedestrian images of an interested identity via textual descriptions. It is challenging due to both rich intra-modal variations and significant inter-modal gaps. Existing works usually ignore the difference in feature granularity between the two modalities, i.e., the visual features are usually fine-grained while textual features are coarse, which is mainly responsible for the large inter-modal gaps. In this paper, we propose an end-to-end framework based on transformers to learn granularity-unified representations for both modalities, denoted as LGUR. LGUR framework contains two modules: a Dictionary-based Granularity Alignment (DGA) module and a Prototype-based Granularity Unification (PGU) module. In DGA, in order to align the granularities of two modalities, we introduce a Multi-modality Shared Dictionary (MSD) to reconstruct both visual and textual features. Besides, DGA has two important factors, i.e., the cross-modality guidance and the foreground-centric reconstruction, to facilitate the optimization of MSD. In PGU, we adopt a set of shared and learnable prototypes as the queries to extract diverse and semantically aligned features for both modalities in the granularity-unified feature space, which further promotes the ReID performance. Comprehensive experiments show that our LGUR consistently outperforms state-of-the-arts by large margins on both CUHK-PEDES and ICFG-PEDES datasets. Code will be released at https://github.com/ZhiyinShao-H/LGUR.