The interface states in ZnO with impurities of transition-metals, Mn, Co, and Cu, were investigated by the DLTS (deep-level transient spectroscopy) measurements in ZnO/PrCoOx/ZnO junctions as model systems of ZnO ceramic varistors and by the SCF-Xα-SW molecular orbital calculations using simplified cluster models. The DLTS signals, correlated to the doping of Mn and Co, are obtained with ZnO/PrCox/ZnO junctions. The signals correspond to the interface states due to the transition-metal doping. Xα calculations indicate that the interface states attributed to the doping of transition-metals, Mn, Co, and Cu, in ZnO are created between the valence band and the conduction band, which consist of transition-metals 3d character. The impurities of transition-metals affect interface states as well as the adsorbed excess oxygen.