The biological recognition of enzymes was the basis of enzyme-based chemical biosensors. It is essential for a biosensor to function under normal operating conditions so that enzymes can catalyze biochemical reactions. The mechanism of a modified enzyme-membrane electrode in a catalytic cycle was described using a mathematical model. The nonlinear terms associated with enzyme kinetics were presented in this model. The Akbari-Ganji's method (AGM) was used to calculate the semi-analytical expressions for species concentration and normalized current. For all possible values of the Thiele modulus, normalized surface concentration of the oxidized mediator, and normalized surface concentration of the substrate, a simple and approximate hyperbolic expression of concentrations of an oxidized mediator, substrate, and reduced mediator were derived. The numerical simulation was then verified using semi-analytical results. The numerical simulation and semi-analytical predictions agreed well with each other.