In this paper, a modified discrete G'/G-expansion method is used to construct exact solutions of Toda lattice equation and Ablowitz-Ladik lattice equations. With the aid of computer symbolic computation, we obtained in a uniform way hyperbolic function solutions, trigonometric function solutions and rational solutions of these two nonlinear lattice equations. When the parameters are taken as special values, some known solutions are recovered. It is shown that the modified method with symbolic computation provides a more effective mathematical tool for solving nonlinear lattice equations in science and enginnering.