The 113I nucleus has been studied using the 58Ni(58Ni,3p) reaction at 250 MeV with the Gammasphere/ Microball facility. Gamma-ray three-and four-fold data gated by charged particle combinations were analyzed. Multipolarities of the γ rays were assigned following the angular correlation measurements. The present study is focused on the high spin properties, where the structure is dominated by 2p-2h excitations across the Z=50 gap. Ten decoupled bands showing the features of smooth band termination were observed; three of those bands are linked to known low-spin states, which allows the identification of configurations by direct comparisons with configuration-dependent cranked Nilsson-Strutinsky calculations. The yrast band, which was linked along with the signature partner, was followed up to (101/2+) and ℏω∼1.3 MeV. The other linked band was a negative-parity band observed up to (95/2-). Tentative configurations for the unlinked bands are discussed. Comparisons with the theoretical results suggest that the band built on a configuration involving the neutron i13/2 intruder orbital originating from the N=6 harmonic oscillator subshell was observed in this experiment.