We consider the discrete Schr{"o}dinger operator $- \Delta_d + V$ defined on the square lattice ${\bf Z}^d$ with $d\geq 2$. Assuming that the potential $V$ is compactly supported, we show that $V$ is uniquely reconstructed from the scattering matrix of a fixed energy. Following the idea for the continuous case, we reduce the problem to one for the D-N map on a bounded domain, where the discrete Rellich type theorem plays a crucial role. This is a joint work with H. Morioka.