According to several conclusions of auxiliary equation, the new infinite sequence solutions of the generalized Fitzhugh-Nagumo equation is constructed in this paper. Firstly, the function transformation and the first integral are presented to obtain the new solutions, Backlund transformation and the nonlinear solution superposition formula of the auxiliary equation. Secondly, through the function transformation, the problem to gain the solutions of the generalized Fitzhugh-Nagumo equation is changed to the problem of obtaining the solutions of the nonlinear ordinary differential equations. Thirdly, some conclusions of the auxiliary equation are employed to construct various new infinite sequence solutions of the generalized Fitzhugh-Nagumo equation with the help of symbolic computation system ‘Mathematica’.