We propose a plasmonic sensor with variable refractive index (RI), which exhibits high sensitivity and extraordinary optical transmission (EOT). Its variable RI is attributed to its dielectric layers and metallic slit arrays. According to simulation results, the third resonant wavelength has a wavelength sensitivity of 800 nm/RIU and an ultra-high transmittance of 0.8 by adjusting the RIs of the upper and lower dielectrics, incident light angle, and structural geometric parameters. With its unique features, the proposed structure holds considerable potential for extensive application to metal–dielectric grating sensors operating at visible and near-infrared frequencies.