To satisfy the engineering requirement of high precision north-finding, the north-finder based on a Rate Biased Ring Laser Gyroscope (RBRLG) and its measurement error come from the scale factor of RBRLG were studied to solve the problem on the scale factor slow change resulted from the inner temperature change and the instability of lock-in region of the RBRLG. Firstly, the change rule of scale factor was researched by a scale factor test. Then, the influence of the scale factor change on the north-finding precision was analyzed by a simulation. Finally, an online first order recursive algorithm was established to estimate the scale factor change according to the periodicity of RBRLG measurement. By introducing the platform angle measurement, the scale factor changes could be obtained. Simulated results indicate that the estimation error for the scale factor of RBRLG is less than 1×10-6 by the proposed algorithm, and the standard deviations of north-finding results caused by the scale factor change decrease to about 2″.The experiment on the north-finder results shows that this algorithm can effectively restrain the north-finding error caused by scale factor change,and the standard deviation is about 24″ for 5 min, which can basically satisfy the requirement of high precision north-finding.