A novel plasmonic sensor based on a D-shaped photonic crystal fiber (PCF) is designed to detect low refractive index changes, and its performance is numerically analyzed using the finite element method (FEM). Unlike the traditional D-shaped PCF, this paper proposes that etching a C-shaped groove channel at the cross-section of the D-shaped fiber and coating the Au layer to excite the plasmons. The design of the C-shaped groove channel can enhance the energy leakage of the fiber core and the coupling strength of both the fiber core and the plasmonic modes. A TiO₂ dielectric layer is added on top of the Au layer to enhance the protection of the metal layer and improve the sensitivity of the sensor. The operating wavelength range of the PCF surface plasmon resonance (PCF-SPR) sensor is extended to the infrared region. The maximum sensitivity obtained from the simulation results is 24236 nm/RIU. The sensor can effectively monitor small changes in a low refractive index and has potential value for biomedical and organic detection and related applications.