This work develops a fully discrete implicit-explicit finite element scheme for a parabolicordinary system with a nonlinear reaction term which is known as the FitzHugh-Nagumo model from physiology.The first-order backward Euler discretization for the time derivative,and an implicit-explicit discretization for the nonlinear reaction term are employed for the model,with a simple linearization technique used to make the process of solving equations more efficient.The stability and convergence of the fully discrete implicit-explicit finite element method are proved,which shows that the FitzHugh-Nagumo model is accurately solved and the trajectory of potential transmission is obtained.The numerical results are also reported to verify the convergence results and the stability of the proposed method.