The photoluminescence of Gd-doped GaN multi-quantum wells (MQWs) is presented and discussed considering the formation of a Gd3+:Nitrogen-vacancy (N-vacancy) complex. A lower energy photoluminescence peak was observed for the Gd-doped GaN MQW sample with respect to the main peak assigned to a neutral donor bound exciton (D0X) of the undoped GaN MQW sample. The X-ray absorption near edge structure spectrum observed at Gd LIII-edge indicates a nitrogen vacancy adjacent to the Gd substituting the Ga ion in Gd-doped GaN MQW sample. Local stresses around the Gd dopants in Gd-doped GaN matrix generated due to the larger diameter of the Gd3+ ion with respect to the Ga3+ ion can be relieved by the creation of vacancies. The lower formation energy of N-vacancies in GaN matrix introduce them as a preferred candidate to relieve the generated stresses. A Gd3+:N-vacancy complex consisting of a Gd3+ ion and the created nitrogen vacancy adjacent to the Gd3+ dopant is likely to form in GaN:Gd matrix. The lower photoluminescence peak energy observed in the Gd-doped GaN MQW sample is assigned to the recombination of an exciton captured at the Gd3+:N-vacancy complex forming a small polaron-like state. A model is presented considering the small exciton-polaron population in defect sites captured around the Gd3+ ions in the Gd-doped GaN.