A finite-difference time-domain approach was used to investigate the excitation of surface plasmons of the circular sub-wavelength apertures on an optical fiber endface. This phenomenon provided the basis of a sensitive liquid refractive index sensor. The proposed sensor is compact and has the potential to be used in biomedical applications, having a sensitivity of (373 ± 16) nm per refractive index unit (RIU) as found through the variation of a reflection minimum with the wavelength.