Hodgkin-Huxley equations are the differential equations that describing the relationship between membrane currents and voltages in nerve fibers.Fitzhugh-Nagumo equations are the simplification of Hodgkin-Huxley equations.The initial value problem of Fitzhugh-Nagumo equations with periodic boundary was discussed.The existence of local solutions to the Fitzhugh-Nagumo equations with periodic boundary was proved by means of the Galerkin method and the theory of ordinary differential equation.And the existence of global solutions was also proved through prior estimates of local solutions.Its uniqueness of the global solutions was proved by using Gronwall inequality.