In order to enhance the accuracy of gyro north seeking system and to make sure how the error sources influence on the final accuracy of the system. Four coordinate systems were established by considering the error sources of the gyro north seeking system; the attitude of the gyro coordinate system versus the geography coordinate system was calculated by way of direction-cosine matrix. Then the component of the local earth rotation rate, which is the function of the initial azimuth angle of the input axis line of the gyro, error sources, and angle positions, was achieved. The initial azimuth angle representation was attained by harmonic analysis method. Aiming at the representation, the error of the azimuth angle was analyzed by error propagation method. Finally the influence of error source over the north seeking system accuracy is achieved.