A photonic crystal fiber (PCF) sensor based on surface plasmon resonance (SPR) with a graphene coating on the cladding is designed for refractive index (RI) detection in the range of 0.3–0.5 THz, especially for liquid bioanalytical sensing. The adjustability of the graphene chemical potential (E f ) enables dynamic tuning of the loss spectra over a wide frequency range with a tuning sensitivity of 570 GHz/eV at the SPR frequency. According to the analysis by the finite element method (FEM), the highest wavelength sensitivity and maximum amplitude sensitivity of 4254.11 µm/RIU and 25.62RIU−1 (n a =1.34) are achieved in the RI range of 1.15–1.35, respectively, together with a resolution of 5.93×10−5RIU. The graphene PCF-SPR sensor boasting high-sensitivity detection in a wide RI range has broad application prospects in multiple fields.