Polarization-induced noise is a dominant noise that seriously hinders the progress of resonator optic gyroscopes. Many countermeasures have been developed but showed insufficient performance. In this paper, we propose a quadrature demodulation technique (QDT) that adopts references of both sine and cosine to demodulate the signal. Theoretical analyses of the polarization effect and QDT are shown, and experimental results are listed and compared. Experimental results are consistent with theoretical analyses. QDT shows great performance in suppressing environment- and polarization-induced phase fluctuation of signal. We also demodulate the intensity-dependent coefficient of 2Ωt term, which is demonstrated effective for compensating polarization-induced intensity noise together with QDT. The scheme shows significant progress in improving long-term stability.