A detection method of resonant fiber optic gyroscope with hollow-core photonic-crystal fiber (HC-RFOG) based on phase-shift keying (PSK) modulation is proposed. The fluctuation of intracavity light intensity and the modulation of the incident light was effectively decoupled, and the influence of the nonlinearity of modulation on the gyro bias stability was reduced. Theoretically, the theoretical gyro bias drift introduced by the nonlinearity of modulation is reduced to below 0.01°/h, without increasing the complexity of the gyro. Compared with the traditional triangle-wave phase modulation method, the method in this paper can effectively suppress the peak difference of the positive and negative first-order harmonics more than 4 times. Ultimately, a HC-RFOG system based on the PSK modulation was built, with which a more than 4 times reduction in the short-term gyro bias drift compared to the traditional triangle modulation and a gyro bias instability of 1.5°/h have been achieved, providing a low-cost and high-performance approach for noise suppression and signal detection in HC-RFOGs.