Abstract: In this paper, We study the global attractor and its properties on infinite lattice dynamical system FitzHugh-Nagumo in a weighted space $l_{\sigma}^2\times l_{\sigma}^2$. We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in $l_{\sigma}^2\times l_{\sigma}^2$. 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.