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 dynamic north-finding scheme based on a FOG, which can be applied to the gyrocompass system, is presented. 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 scheme is organized by the developed algorithm. Simulation results are included to verify the performance of the proposed scheme.