A method to estimate the efficiency of relative intensity noise subtraction for a Fiber Optic Gyroscope (FOG) was proposed, and the estimation result could be used to improve the reliability of relative intensity noise subtraction of the FOG. Theoretical analysis shows that the efficiency of relative intensity noise subtraction of the FOG is highly dependent on the cross-correlation between the outputs of FOG and coupler. By proposed method,the experiment on a high precision interferometric FOG was performed, and obtained results show that when the cross-correlation coefficient is 0.91, the variance of the noise after subtraction reduces to 17.16%.However when the cross-correlation coefficient is 0.28, that of the noise after subtraction goes up to 143.18%. These results are coincident with that of theoretical analysis.By utilizing this method,the cross-correlation between the outputs of FOG and coupler improves the reliability of the intensity noise subtraction.