We study -derivations of a group ring RG of a finite group G over an integral domain R with 1. As an application we extend a well known result on derivation of an integral group ring to -derivation on it for a finite group G with some conditions on σ and τ. In the process of the extension, a generalization of an application of Skolem-Noether Theorem to derivation on a finite dimensional central simple algebra has also been given for the -derivation case.