Back by a rigid cavity filled with a layer of porous layer, the sound absorption performance of a micro-perforated panel (MPP) can be enhanced in comparison with other resonance based sound absorbers. In this paper, a theoretical model of a finite flexible MPP back by a rigid air cavity filled with a fibrous porous material is developed to predict normal sound absorption coefficients. Displacements of MPP and sound pressure field in fibrous porous material and acoustic cavity are expressed using a series of modal functions, and the sound absorption coefficients of MPP system are obtained. Additionally, comparison of energy dissipation by MPP and fibrous material is performed to identify effects of a fibrous material on the sound absorption of a MPP. As expected, at anti-resonance frequency of an MPP, the fibrous material provide an alternative energy dissipation mechanism.