In the gyrocompass system, the use of the fiber optic gyroscope(FOG) makes this traditional system considerably attractive because it has strong points in terms of weight, power, warming-up time, and cost. In this paper, a novel digital north-finding method based upon an FOG, which can be applied to the gyrocompass system, is proposed. The analytical model for the earth signal of the FOG is described, and the earth signals passed through lock-in amplifiers are modeled. Additionally, a north-finding algorithm using two lock-in amplifier outputs is developed, and the proposed method is organized by the developed algorithm. Simulation results are included to verify the performance of the proposed method.