Biomedical sensor that sense different molecules with a high refractive index sensitivity is proposed in this work. Plasmonic nanospiral antenna is mounted on a top surface of an optical fiber to reflect the incident optical signal back to the fiber. The reflected signal depends on the nanospiral antenna material, dimensions and the surrounding medium. Using streptavidin molecule, the nanospiral antenna have been simulated based on finite difference time domain method to optimize its dimensions. The optimum dimensions are 10 nm, 55 nm and 40 nm for inner-outer thicknesses and height respectively. The introduced biosensor can detect different molecules based on surface plasmonic resonance, which depends on the shifting of the peak wavelength according to the molecules type. The detected molecules are Streptavidin, Urease, Uricase molecules and Glucose oxidase and Cholesterol oxidase enzymes with a high sensitivity. The maximum refractive index sensitivity is obtained when sensing cholesterol oxidase molecules with 3028 nm/RIU at 3.58 μm peak wavelength. Figure of merit and quality factor are also calculated for all detected molecules. Finally, electric field and optical power, before and after binding, of the reflected signal are illustrated and discussed.