In this paper,We study the global attractor and its properties on infinite lattice dynamical system FitzHugh-Nagumo in a weighted space l2σ × l2σ.We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in l2σ × l2σ.Then we get a bounded absorbing set,which suggests the existence of global attractors.Finally,we study the uniform boundedness and the upper semicontinuity of the global attractor.