We design and numerically investigate a perfect narrow band absorber based on a metal-metal-dielectric-metal structure which consists of periodic metallic nanoribbon arrays. The absorber presents an ultra narrow absorption band of 1.11 nm with a nearly perfect absorption of over 99.9% in the infrared region. For oblique incidence, the absorber shows an absorption more than 95% for a wide range of incident angles from 0 to 50°. Structure parameters to the influence of the performance are investigated. The structure shows high sensing performance with a high sensitivity of 1170 nm/RIU and a large figure of merit of 1054. The proposed structure has great potential as a biosensor.