This paper presents the design and analysis of a surface plasmon resonance (SPR) sensor in a photonic crystal fiber (PCF) platform, where graphene is used externally to attain improved sensing performance for an aqueous solution. The performance of the proposed sensor was analyzed using the finite element method-based simulation tool COMSOL Multiphysics. According to the simulation results, the proposed sensor exhibits identical linear characteristics as well as a very high figure of merit (FOM) of 2310.11 RIU−1 in the very low detection limit of 10−3. The analysis also reveals the maximum amplitude sensitivity of 14,847.03 RIU−1 and 7351.82 RIU−1 for the x and y polarized modes, respectively, which are high compared to several previously reported configurations. In addition, the average wavelength sensitivity is 2000 nm/RIU which is comparatively high for the analyte refractive index (RI) ranging from 1.331 to 1.339. Hence, it is highly expected that the proposed PCF-based SPR sensor can be a suitable candidate in different sensing applications, especially for aqueous solutions.