In rice and wheat, glume and floral organ length are positively correlated with grain size, making them an important target to increase grain size and potentially yield. The wheat subspecies Triticum ispahanicum is known to develop elongated glumes and floral organs as well as long grains. These multiple phenotypic effects are controlled by the P2 locus, which was previously mapped to wheat chromosome 7B. Using three mapping populations, we show that the long glume locus P2 does not map to chromosome 7B, but instead maps to a 1.68 Mbp interval on chromosome 6A. Within this interval, we identified SVP-A1, a MADS box transcription factor which is the direct ortholog of the maize gene underlying the pod corn Tunicate locus and is a paralog to the T. polonicum elongated glume P1 gene. In T. ispahanicum, we identified a unique allele which has a 482-bp deletion in the SVP-A1 promoter and is associated with ectopic and higher expression of SVP-A1 in the elongated glumes and floral organs. We used near-isogenic lines (NILs) to show that P2 has a consistent positive effect on the length of glume, lemma, palea, spike and grain. Based on the mapping data, natural variation, biological function of SVP genes in cereals and expression analyses, we propose the MADS-box transcription factor SVP-A1 as a promising candidate for P2.