To investigate the output stability of a high power fiber ring laser system containing a birefrigent fiber, a kind of vector modulation instability — sideband polarization instability (SPI) was proposed. Nonlinear Schrdinger equations describing the polarized light propagating in a unidirectional fiber ring laser were deduced based on the methods of polarization instability and sideband instability. General coupling equations governing the evolution of sidebands caused by SPI in strongly birefringent fiber ring lasers were derived. Analytical solution was obtained for the case when the signal light was polarized along one principle axis of the fiber. The results show that in normal dispersion region, the sideband gain induced by perturbations to signal light propagating along the principle axis evolves in a saw-tooth manner, and approaches a fixed value with the increase of signal power.