A high-sensitivity refractive index sensor is demonstrated for the first time, near the ultraviolet (UV) wavelength region using a Si3N4-subwavelength grating (SWG) with a normal incident optical geometry. Using the eigenmode within the Si3N4-SWG, a high sensitivity for the refractive index is expected by finite-difference time-domain calculation, without an oblique incident geometry. The proposed SWG is fabricated and the high-sensitivity refractive index sensor operating near the UV wavelength is experimentally and successfully developed. The normal transmitted intensity through the fabricated SWG varies considerably with slight changes in the refractive index. The experimental sensitivity of the SWG attained 1240% per refractive index unit (RIU) and the sensitivity shows good agreement with the calculation. These experimental results suggest that our refractive index sensor with a normal incident geometry can measure a refractive index change of 8.06×10−4 RIU, if the optical detection system can measure an intensity change of 1%.