We theoretically propose a simple ultra-narrow multi-band perfect absorber for sensing applications. The perfect absorber consists of periodically arranged metallic nanodisks etched with regular prismatic holes standing on the dielectric-metal bi-layer films. Multiple ultra-narrow perfect absorption bands are obtained in the near-infrared region with the maximum bandwidth less than 21 nm and the intensity as high as 99.86%. The ultra-narrow multi-band perfect absorption originates from the synergy of localized surface plasmons, propagating surface plasmons and lattice resonances. The perfect absorber also presents other significant advantages, e.g. polarization insensitivity and high sensitivity of surrounding environments. Moreover, the prominent sensing performance for detecting the trace amounts of glucose in water is demonstrated. These features make it a promising candidate with great potential in the fields of perfect absorbers, plasmonic sensors, filters and multiplexing binding bio-molecular detection.