An idea of the surface plasmon resonance (SPR) has been utilized for the design of highly sensitive sensors based on the wagon-wheel fiber technology. Such sensors are sensitive to changes in the refractive index of sample analyte. In this study, a three-strut wagon-wheel structure, coated with the gold layer of nano-sized thickness, has been proposed as the SPR sensor. Finite element method is employed to simulate and tune the proposed SPR’s design, which leads to a highly sensitive and multichannel plasmonic sensor with the ability for a dual reading on a single analyte or simultaneous identification of two analytes. In this design, suitable thickness values for the gold layer and core struts are determined. Sensitivities of the detector due to the first resonance peak, second resonance peak, and the difference in resonance peaks are calculated to be 1120 nm/RIU, 1540 nm/RIU, and 420 nm/RIU, respectively, when analytes are placed in all three channels of the fiber. Sensitivity of the detector with respect to the second resonant peak for analyte in Channels 2 and 3 is also found to be 1252 nm/RIU when Channel 1 is filled with the reference. The sensitivity and resolution of the sensor increase as the refractive index of the analyte increases by almost a linear proportion. If the sensor is utilized to detect the difference in two peaks, it would substantially reduce the noise, and the best result is expected. The thicknesses of the struts and the gold layer are proper parameters to be tuned in designing the detector.