In this paper, a dual-core D-shaped photonic crystal fiber (PCF) based surface plasmon resonance (SPR) refractive index sensor coated by tantalum in two segments has been designed and studied. The sensing performance of the proposed sensor in the visible to near infrared (800–1300 nm) region for detecting low refractive index analytes is numerically investigated. The finite element method (FEM) is used to design and study the influence of different structure parameters by the optical loss spectrum on the sensing performance of the sensor. The chemically stable plasmonic material tantalum (Ta) is used to produce excitation between the core and plasmonic modes. On a pure silica (SiO2) substrate, a rectangular structured dual core is used to facilitate the coupling strength between the cores 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 10400 nm/RIU (Refractive Index Unit) for analyte refractive indices ranging from 1.25 to 1.39. The sensor also attains a maximum figure of merit (FOM) of 35.25 /RIU and fine refractive index resolution of 9.615 × 10 −6 RIU. Owing to Ta chemical stability, low cost, simple structure, high sensitivity, relatively high FOM and improved sensing resolution, the proposed sensor is suited for real-time, inexpensive and accurate detection of biomedical and biological analytes, bimolecular, and hazardous corrosive gases.