Theoretical analysis of noise reduction by a membrane-duct system is presented. When acoustic waves propagate in the membrane-duct, the part of membrane is also excited and its motion is coupled with interior medium. For an infinite plane membrane-duct system, a simple coupled governing equation is derived and solved. One of the characteristics of dispersion relation is that evanescent waves occur below critical frequency. Attaching damping materials to the membrane may improve the absorption efficiency of acoustic energy. The results show that the membrane-duct system can be applied to diminish and absorb low frequency noise in duct instead of passive muffler, such as simple expansion chamber or absorption material.