An all-digital closed-loop (ADCL) signal processor for an open-loop FOG was developed to replace the analog circuitry of a Digital Phase Tracking (DPT) signal processor with new digital circuitry. When the ADCL signal processor without a stabilizer for fiber phase modulator (FPM) was attached to the FOG, temperature drift of FOG was about 0.26$mu$rad/$^{circ}C$, which makes the FOG unusable in medium or higher-grade applications. This drift was due to variations of phase modulation amplitude and phase delay of the FPM. The stabilizer controls its phase modulation amplitude and phase delay by regulating the ratio of harmonics of the FOG output. Thus, the stabilizer reduces the drift of the FOG to negligible.