The acoustic pathway in the enclosure of small headphones is very narrow. Therefore, the speed of sound propagation and the phase change because of the air viscosity. We have developed a new finite element method that considers the effects of damping due to air viscosity in the sound pathway. The new finite element method is obtained by improving the finite element method proposed by Yamaguchi for porous sound-absorbing materials. Moreover, we have attempted to obtain a numerical calculation of damping due to air viscosity by using the proposed finite element method.