The aim of this talk is to study the finite-dimensional approximations of the nonautonomous lattice dynamical systems of the form \begin{equation} u_{i}`=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z). \end{equation} We show that the finite-dimensional approximations for are uniformly dissipative. The upper semi-continuous convergence of the attractors of the finite-dimensional approximations is established.