Taking account of shot noise, thermal noise, dark current noise, and intensity noise that come from broad band light source, the dependence of the random walk coefficient of fiber optic gyroscope (FOG) on bias phase and light power is studied theoretically and experimentally. It is shown that with different optical and electronic parameters, the optimal bias phase is different and should be adjusted accordingly to improve the FOG precision. By choosing appropriate bias phase, the random walk coefficient of the aim FOG is reduced from 0.0026 to 0.0019 deg./h^(1/2).