The β decay of 129 Cd, produced in the relativistic fission of a 238 U beam, was experimentally studied at the RIBF facility at the RIKEN Nishina Center. From the γ radiation emitted after the β decays a level scheme of 129 In was established comprising 31 excited states and 69 γ-ray transitions. The experimentally determined level energies are compared to state-of-the-art shellmodel calculations. The half-lives of the two β-decaying states in 129 Cd were deduced and the β feeding to excited states in 129 In analyzed. It is found that as in most cases in the Z<50, N ≤82 region both decays are dominated by the ν0g 7/2 → π0g 9/2 Gamow-Teller transition, although the contribution of first-forbidden transitions cannot be neglected.