The resonator optic gyro (ROG), which utilizes a resonance frequency change due to the Sagnac effect, is a promising candidate for the next generation inertial rotation sensor. In this paper, we first analyzed the signal detection theory and made the demodulation curve modeling. Second, the ROG demodulation test system is set up using the laser frequency modulation spectroscopy technique. The resonance curve of the resonator is detected by the photodiode (PD) and then demodulated by the LIA. By testing at λ=1550nm, and the free spectral range (FSR), the full width at half maximum (FWHM), the depth and the finesse of resonance are 2191.41MHz, 65.55MHz, 0.9 and 33.43 respectively. Calculated from the demodulation signal, the dynamic range of the gyro is from +2.04×103rad/s to -2.04×103rad/s. The slope K1 of the linear part in the demodulation signal is estimated to be 0.8×10-7V/Hz. A basic agreement between experimental results and theoretical calculated values was achieved.