The invention discloses a double-ring parallel resonant gyro system and a double-closed-loop digital demodulation method thereof. The system comprises a tunable laser, outgoing light of the tunable laser is split into clockwise light and anticlockwise light through a signal beam splitter, the clockwise light and the anticlockwise light sequentially enter an acousto-optic frequency shifter, an electro-optic modulator, an optical fiber coupler, a hollow photonic band gap optical fiber resonant cavity, a photoelectric detector and a digital lock-in amplifier respectively, and frequency closed-loop feedback is formed through the tunable laser and the acousto-optic frequency shifter respectively. According to the double-ring hollow photonic band gap optical fiber structure, clockwise and anticlockwise light waves are respectively propagated in the independent resonant cavities without mutual influence, so that the temperature stability is improved, and nonreciprocal effect noises such as anoptical Kerr effect, Rayleigh backscattering and the like are effectively inhibited. According to the double-closed-loop digital demodulation method, optical frequencies in a clockwise optical path and an anticlockwise optical path are locked at respective transmission resonant frequencies, so that the system works in a linear region, and the linear range of angular velocity detection of the system and the linearity of a scale factor are effectively improved.