For the first time a mathematical modelling of the enzymatic glucose membraneless fuel cell with direct electron transfer has been reported. The niche of this mathematical modelling is the description of the new Homotopy perturbation method to solve the nonlinear differential equations that describes glucose concentration and hydrogen ions respectively. The analytical results of an enzymatic fuel cell should be used, while developing fuel cell, to estimate its various kinetic parameters to attain the highest power value. Our analytical results are compared with limiting case results and satisfactory agreement is noted. The influence of parameters on the concentrations are discussed. (C) 2016 Elsevier B.V. All rights reserved.