In this study, an integrated resonant fiber optic gyroscope (R-FOG) scheme that employs a hybrid photonic crystal fiber (PCF) resonator is proposed to suppress the polarization-fluctuation noise of R-FOG. The hybrid PCF resonator, which exhibits a high polarization extinction ratio and good temperature stability, is primarily composed of a specially designed PCF and single polarization fiber (SPF). To reduce the resonator loss, the mode field diameter of PCF is modified to become consistent with that of SPF. Further, the fusion loss of the two types of fibers is controlled within 0.1 dB. In addition, the fineness of the hybrid PCF resonator is 13.2. A double closed-loop R-FOG system is set up based on the hybrid PCF resonator, and its performance is experimentally studied. The results denote that the R-FOG system exhibits small polarization-fluctuation error characteristics. The white noise dominates the output at an integration time of 300 s when a bias stability of 0.25 (°)·h ^-1 is achieved. Within the dynamic range from -240 (°)·s ^-1 to 240 (°)·s ^-1, the scale-factor nonlinearity of the double closed-loop R-FOG system is observed to be 2.3×10 ^-4. The performance of the double closed-loop R-FOG system is better than that of a single closed-loop R-FOG system.