A many-body theory for a multi-orbital tight-binding model is developed by taking account of local three-body correlations. The theory is applied to the antiferromagnetic NiO. The multiple structures of three-particle states are fully taken into account. It is shown that the self-energy correction leads to the correct value of the band gap, the orbital character of the valence band top which is consistent with the charge-transfer insulator, and the presence of the satellite intensities. The quasiparticle band is obtained in good agreement with the angular-resolved photoemission data of NiO.