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The excitonic insulator phase is one of the novel electronic ground states driven by many-body interactions. Despite its theoretical proposal about 60 years ago, its material realization is still unclear. Ta₂NiSe₅ is a strong candidate, exhibiting a temperature-driven phase transition without any other competing phase such as the charge-density-wave. Experimental evidence so far includes an anomalous increase of the electric resistivity, the flat valence band maximum, and optical gap measurements. We provide further evidence of the excitonic insulator phase in Ta₂NiSe₅ using scanning tunneling microscopy/spectroscopy. At 78 K, the single-particle gap is measured as 300 meV and the orbital characters at the valence band maximum (-175 meV) are inverted from the high-temperature phase. These results indicate the strong interband (or electron-hole band) interaction in the gap opening, which is in a good agreement with the excitonic scenario. Moreover, our model calculation reveals that the non-interacting phase in Ta₂NiSe₅ has a semimetallic band structure, implying the excitonic condensation in Ta₂NiSe₅ is close to the Bardeen-Cooper-Schrieffer (BCS) regime.