In this letter, we propose a novel approach to develop a highly sensitive surface plasmon resonance (SPR) based fiber optics biosensor. The sensor comprises a dual-drilled channel (DDC) with gold-nanowire (AuNW) contained in each channel to excite the plasmon modes. The SPR effect between the core guided mode and the surface plasmon polariton (SPP) modes of the DDC is used to evaluate the sensing response with respect to different analytes. The sensing performance, coupling characteristics, and the fabrication tolerance of the sensor are numerically analyzed and characterized by using a full-vectorial Finite Element Method (FEM). The designed sensor shows a minimum sensitivity of 3150 nm/RIU for refractive index (RI) = 1.310. While, the sensor exhibits an extremely high sensitivity varying from 10250 nm/RIU to 90500 nm/RIU for RI varied over the range of 1.370 to 1.400. Various structural parameters, e.g., separation of the channel from the core, the radius of the AuNW, the fabrication tolerance, etc., have been studied in this work. In addition, the possible fabrication steps of such a design have been discussed indicating its simple practical realization.