In this paper, mathematical models of biofilteration of mixtures of hydrophilic (methanol) and hydrophobic (α-pinene) volatile organic compounds (VOC's) are discussed. This model is based on the system of diffusion equations containing a nonlinear term related to the Michaelis-Menten kinetic of the enzymatic reaction. The model describes the mass transfer in air-biofilm interface and chemical oxidation in the air stream phase. An approximate analytical expression of concentration profiles of methanol and α-pinene in air stream and bio-film phase have been derived using the Adomian decomposition method for all possible values of parameters. Furthermore, in this work, the numerical simulation of the problem is also reported using the Matlab program to investigate the dynamics of the system. Graphical results are presented and discussed quantitatively to illustrate the solution. Good agreement between the analytical and numerical data is noted.