We observe the phenomenon of priority oscillation of the unexpected σ-polarization in high-power Nd:YVO 4 ring laser. The severe thermal lens of the σ-polarized lasing, compared with the π-polarized lasing, is the only reason for the phenomenon. By designing a wedge Nd:YVO 4 crystal as the gain medium, the unexpected σ-polarization is completely suppressed in the entire range of pump powers, and the polarization stability of the expected π-polarized output is enhanced. With the output power increasing from threshold to the maximum power, no σ-polarization lasing is observed. As a result, 25.3 W of stable single-frequency laser output at 532 nm is experimentally demonstrated.