Bonding and anti-bonding modes of plasmon coupling effects are numerically investigated in TiO2-Ag core-shell nano dimers. First, splitting phenomena of the coupled anti-bonding modes are observed under the longitudinal polarization when the distance between the monomers decreases to a certain level. Second, one of the split resonance modes is identified to be formed by the dipole anti-bonding mode of the monomers from charge density distribution patterns. Those split modes have similar redshift behaviors as the coupled dipole bonding modes in the same situations. Furthermore, the intensities of those anti-bonding modes weaken with decreasing distance between the monomers, because of the interaction of the induced dipole moment in the monomers and the charge distribution variation on the facing surfaces of the gap by the coulomb attraction. Other split bands are the higher-order mode (octupole-like or triakontadipole-like), which do not have obvious peak-shift behavior, and the intensities have very little attenuation with decreasing distance. Finally, the coupling of the bonding and anti-bonding modes under the longitudinal polarization is symmetric (bonding).