This study builds an optical fiber surface plasmon resonance (SPR) sensor theoretical model with four-layered media based on the Kretschmann structure. Simulation results show that the phase difference between p- and s-polarized components changes almost linearly with the refractive index in the section of 1.333--1.336, deriving the sensor measurement formulas of optical fiber SPR. Using a dual-frequency He-Ne laser, an optical fiber SPR measurement system with heterodyne interferometry based on a common optical path structure is presented. A higher measurement resolution of the proposed sensor can be achieved through the signal processing method of phase demodulation. The experimental calibration data of glycerin solution show that the measurement results are consistent with the theoretical analysis. Results are in good agreement with those obtained by other methods, and the error of refractive index between the two methods is less than 8.0×10 -5. The proposed sensor can be applied in many fields such as environment detection, food safety, drug screening, and clinical medicine.