Flowering time is a critical agronomic trait that has strong effects on crop yields. Auxin signaling pathway plays an important role in various development processes, such as flowering, grain development. However, no Aux/IAA gene had been reported to have functions involving in wheat flowering time. Here, we systematically performed genome-wide identification, classification, domain distribution, exon-intron structure, chromosome locations and global expression pattern of Aux/IAA gene family in 14 plant genomes (including Triticum aestivum). A phylogenetic model was proposed to infer the Aux/IAA evolutionary history involving in a central exon-intron structure “2121” during evolution. Overexpression of TaIAA15-1A caused an early flowering time in Brachypodium. RNA-seq analysis showed that TaIAA15-1A overexpression alters various pathways including phytohormone signaling pathway, flowering-related pathway, and polyamine biosynthesis pathway. Screening of auxin response factor (ARF) genes identified BdARF16 that interacted with TaIAA15-1A. Exogenous polyamine (spermidine and spermine) treatments promoted early flowering and (putrescine and DCHA) delayed flowering time of WT plants. Our finding will provide insights on mechanisms of Aux/IAAs gene family and TaIAA15-1A, illustrating the potential during crop improvement programs.