[Objective] Auxin is one of the most important phytohormone and regulates many biological processes in plant. Small auxin up RNAs，which belong to a kind of auxin early response gene, plays an key role in plant cell elongation. However, the function of SAURs on cotton fiber development is not clear. [Methods] In this study, a new gene encoding SAUR protein was cloned from cotton (Gossypium hirsutum), and named GhSAURX. Then, expression pattern, subcellular localization, phenotype identification of transgenic Arabidopsis, and expression analysis of auxin-related genes were performed to explore Its function. [Results] Phylogenetic analysis revealed that GhSAURX have close relationship with SAUR76, SAUR77 and SAUR78 in Arabidopsis, and belonged to SAUR76 subfamily. qPCR showed that the highest expression level of GhSAURX is observed in fiber of 15, 18 and 21 DPA, when fiber elongated fast. Meanwhile, GhSAURX showed much higher expression level in variety with long fiber than that in variety with short fiber. Analysis of subcellular localization indicated that GhSAURX distributed in cytoplasm and nucleus. Overexpression of GhSAURX promoted the elongation of primary root and hypocotyl under dark condition in Arabidopsis, and elevated the expression auxin related genes, such as YUCCA6, ARF7 and PIN4. [Conclusion] Our results indicated that GhSAURX functioned in the cell elongation mediated by auxin.