A quadrature demodulation algorithm for large dynamic range measurement of open-loop fiber optic gyroscope is studied in this paper. The interference signal is directly sampled every π/6 every cycle, and 12 sampling points are obtained for phase demodulation. The large dynamic range measurement of open-loop fiber optic gyroscope is realized by using fringe counting method. The relationship between the sampling phase error of phase modulator driving signal and interference signal of open-loop fiber optic gyroscope system and the demodulation error of quadrature demodulation algorithm is analyzed in detail. The evaluation parameters of modulation depth error E_M and modulation initial phase error E_W are constructed by using the extracted 12 sampling points, and the sinusoidal modulation signal parameters are feedback controlled to ensure the demodulation accuracy. The results show that in order to make the phase demodulation error of open-loop fiber optic gyroscope within ±10^-6 rad (scale factor is 1.134 s, gyro output angular velocity error ±0.18 (°)/h), the error of modulation frequency f_e of sinusoidal modulation signal should be less than ±0.072% (97.31 kHz), and the error of voltage peak to peak V_π should be less than ±0.1% (3.654 V), the modulation initial phase error should be less than ±16.226 mV and the modulation depth error should be less than ±12.483 mV, and the digital sampling phase error should be less than 5.625×10^-4 rad.