A dual-resonance-peak photonic crystal fiber–surface plasmon resonance (PCF-SPR) refractive index (RI) sensor is designed for different wavelength ranges. The first resonance peak of the sensor is distributed in the wavelength range of 700–2350 nm, while the second peak is distributed in the range of 2350–5550 nm. In addition to detecting analytes using the full spectrum of constraint losses (CLs), it is also possible to use a single resonance peak to achieve the detection of analytes. By systematically optimizing the nanowire diameter, the diameter of the inner and outer layer air hole, the width of the groove, the polishing depth, and the distance from the outer layer air hole to the fiber core, the optimal structure of the sensor is finally determined. In this study, the sensor was studied by numerical analysis, and the characteristics of the sensor were evaluated by wavelength detection technology. The results show that within the RI range of 1.24–1.37, the sensor has a maximum wavelength sensitivity (WS) of 54700 nm/RIU for detecting the RI of analytes. Within the above refractive index range, the regression coefficient R2 of the dual-peak-resonance wavelength is 0.99993, ensuring the accuracy of the estimated resonance wavelength of the sensor. In addition, the sensor can also use dual-peak-shift sensitivity (DPSS) to detect the refractive index, which is a relatively new sensing technology. The maximum DPSS of the sensor is 95300 nm/RIU. Due to its high sensitivity and unique dual-peak characteristics, this sensor has wide application prospects in medical diagnosis, environmental monitoring, food safety, and other fields.