We propose and numerically characterize the optical characteristics of a novel photonic crystal fiber (PCF) based surface plasmon resonance (SPR) sensor in the visible to near infrared (500-2000 nm) region for refractive index (RI) sensing. The finite element method (FEM) is used to design and study the influence of different geometric parameters on the sensing performance of the sensor. The chemically stable plasmonic material gold (Au) is used to produce excitation between the core and plasmonic mode. On a pure silica (SiO2) substrate, a rectangular structured core is used to facilitate the coupling strength between the core and the surface plasmon polariton (SPP) mode and thus improves the sensing performance. By tuning the geometric parameters, simulation results show a maximum wavelength sensitivity of 58000 nm/RIU (Refractive Index Unit) for the x polarization and 62000 nm/RIU for the y polarization for analyte refractive indices ranging from 1.33 to 1.43. Moreover, we characterize the amplitude sensitivity of the sensor that shows a maximum sensitivity of 1415 RIU-1 and 1293 RIU-1 for the x and y polarizations, respectively. To our knowledge, this is the highest sensitivity for an SPR in published literature, and facilitates future development of sensors for accurate and precise analyte measurement. The sensor also attains a maximum figure of merit (FOM) of 1140 and fine RI resolution of 1.6 × 10-6. Owing to strong coupling strength, high sensitivity, high FOM and improved sensing resolution, the proposed sensor is suited for real-time, inexpensive and accurate detection of biomedical and biological analytes, biomolecules, and organic chemicals.