The effect of the large power depletion of the fundamental wave in the phase-matched polarization on the stability of the second-harmonic wave output from an intracavity frequency-doubled ring laser is discussed. It has been demonstrated that the instability resulting from the unbalanced power depletion of the fundamental waves can be eliminated by using a wedge laser rod. The function dependence of the wedge angle and the laser power is concluded. An intracavity frequency-doubled ring laser with a wedge Nd:YVO 4 laser crystal and a LBO doubler is designed and built. Comparing with similar lasers but without using the wedge laser crystal, the frequency-conversion efficiency, the power stability and the polarization purity of the second-harmonic wave output from the laser with a wedge laser rod are significantly improved. The single-frequency green laser of 6.5W at 532nm, with the polarization degree more than 500:1 and the power stability better than ±0.3% for 3h, was experimentally achieved.