A photonic crystal fiber (PCF) sensor based on surface plasmon resonance with a gold film coating is designed and investigated for detecting the analytes with a low refractive index (RI). The critical geometry parameter is optimized by the finite element method to increase the sensitivity of the sensor. An open-ring structure with a 70-nm-thickness gold film coated on the inner surface is located on the left and right sides of the PCF sensor, and its angle is equal to or greater than 90 deg. The spectral and amplitude sensitivities are numerically calculated to evaluate the sensing performance of the proposed sensor. The simulation results indicate that the maximum and average sensitivities are 68,000 and 9583  nm  /  RIU, respectively. The resolution is a critical parameter for assessing the sensing performance of the sensor with a maximum value of 1.47  ×  10^−  6  RIU. The simulation results show that the RI of analytes that the sensor can detect ranges from 1.20 to 1.31. Therefore, the sensor possesses wide application prospects in the field of biosensors.