We realize a transmissive single-beam-splitter resonator optic gyro based on a hollow-core photonic-crystal fiber (HCPCF), utilizing a micro-optical coupler formed by pairs of lenses and one filter, which is a new type of resonator fiber optic gyro based on the HCPCF (HC-RFOG). We build a mathematical model of the polarization noise based on the transfer function of this novel transmissive single-beam-splitter resonator. We construct a HC-RFOG and simulate and validate the effects of polarization noise on the gyro system. In addition, we apply an effective method to suppress the polarization noise and prove its efficacy through experiments. The bias stability of the gyro system is successfully improved from 25 °/h to 2 °/h, which indicates a remarkable advance of performance of HC-RFOG.