The theory of the non-critical phase-matched KTPⅡcrystal placed in corner-cube resonator was discussed. It was found that there existed eigen mode of special polarization azimuth to meet the non-eritical phase-matched condition. Experiment based on Cr4+:YAG passively Q-switched intracavity optical parametric oscillator (OPO) was performed, and the conversion efficiency was higher than that in the plane-parallel resonator. The effects of the transmission of Cr4+:YAG crystal upon the intracavity power density were analyzed, and the relationship of signal-pulse energy versus pump energy with different transmission of Cr4+:YAG crystal was obtained. The performance of OPO laser was much better than that in plane-parallel resonator for the electro-optical efficiency can be up to 0.25%. A compact and efficient OPO was designed, the pump energy threshold was 4.7 J, the pulse energy was 11.8 mJ, the pulse width was 6.9 ns, the beam divergence was 7 mrad and the pulse stability was 5%.