In this paper，a synchronous north-finding algorithm based on a relative azimuth constraint is proposed for a single-axis forward and reverse continuous rotation modulation north-finding system. Based on velocity observations，the relative azimuth error in the north-finding process was used as the observation measurement，and the convergence speed of the azimuth error angle was improved. First，the influence of the gyroscope bias error，gyroscope scale factor error，and goniometric mechanism on the north-finding accuracy of uniaxial forward and reverse continuous rotation was analyzed，and a compensation scheme was developed. Subsequently，forward rotation and reversal were used as two north-finding states to construct a systematic error model under the condition of a static base，and a measurement equation was established based on the velocity and relative azimuth error. Finally，the experimental data verified the effectiveness of the algorithm，and the results showed that the algorithm can effectively improve the accuracy and shorten the accuracy of the north search. The accuracy of the north-finding in 5 min is better than 10"（1σ），which has significant engineering practical value.