The β-decay scheme of 138Te and the level structure of 138I is reported for the first time. The experiment was performed at the Radioactive Isotope Beam Factory of RIKEN, as one of the EUROBALL-RIKEN Cluster Array campaigns. Secondary radioactive ions, including 138Te and 138Sb, were produced by the in-flight fission of a 238U beam with the energy of 345 MeV per nucleon. From the β decay of 138Te, the level scheme of 138I was supplemented with new spin and parity assignments, such as the low-lying negative-parity states and a positive-parity 1+ state. This 1+ state can be interpreted as being associated with the π0h11/2⊗ν0h9/2 partner orbital configuration populated by the Gamow-Teller transition between a neutron in the 0h9/2 orbital and a proton in the 0h11/2 orbital. Details of the structure of 138I are discussed in terms of the proton-neutron interactions and Gamow-Teller transition strength within the theoretical context of shell-model calculations.