The theoretical analysis of the steady-state amperometric oxidase enzyme-membrane electrode is developed. The model is based on diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. We employ the homotopy perturbation method (HPM) to solve the system of coupled non-linear diffusion equations for the steady-state condition. Simple and approximate polynomial expressions of concentration of oxygen (mediator), substrate and flux are derived for all possible values of parameters phi (Theiele modulus), B(O) (normalized surface concentration of mediator), and B(S) (normalized surface concentration of substrate). Furthermore, in this work the numerical solution of the problem is also reported using SCILAB program. The analytical results are compared with the numerical results and found to be in good agreement. (C) 2011 Elsevier B.V. All rights reserved.