The relationships of mean output difference and distribution index of ring laser gyroscope with the intensity of random noise are obtained. Based on the relationships, the way to design random noise is produced and exampled. The results show that pure random noise is no good to reduce the error because the introduction of random noise will reduce the measurement scope of ring laser gyroscope sharply or enlarge the output difference of ring laser gyroscope heavily. However, superimposing random noise on periodical dither signal can reduce the error deeply while the measurement scope of ring laser gyroscope is not reduced and increasing sample period moderately can reduce the enlarged output difference.