In this project, Green’s function method is applied to obtain the analytic solution of non-homogenous heat equation defined on a given domain with appropriate initial and/or boundary conditions. With this purpose, firstly the theory, how to get Green's function for a heat equation, in -dimensional infinite space is discussed, and then using method of images, how this infinite domain Green's function, should be modified, so that it can serve for semi- infinite and finite domains is shown. Applications of the method are illustrated by examples for one-dimensional non-homogenous heat equation problems with given domains, namely, infinite, semi-infinite and finite domains