We have performed angle-resolved photoemission spectroscopy on EuIn2As2 which is predicted to be an axion insulator in the antiferromagnetic state. By utilizing soft-x-ray and vacuum-ultraviolet photons, we revealed a three-dimensional hole pocket centered at the Γ point of bulk Brillouin zone together with a heavily hole-doped surface state in the paramagnetic phase. Upon entering the antiferromagnetic phase, the band structure exhibits a marked reconstruction characterized by the emergence of a "M"-shaped bulk band near the Fermi level. The qualitative agreement with firstprinciples band-structure calculations suggests the occurrence of bulk-band inversion at the Γ point in the antiferromagnetic phase. We suggest that EuIn2As2 provides a good opportunity to study the exotic quantum phases associated with possible axion-insulator phase.