The dynamic magnetic susceptibility is calculated for bulk bcc iron, a supported monolayer Fe/W(110) and corresponding free standing Fe monolayer. The calculational approach is based on linear response density functional theory formulated within the framework of Korringa-Kohn-Rostoker Green's function method. The calculated susceptibilities are analyzed in terms of dispersion and damping of spin-waves. The results for bulk Fe are in good agreement with experiment and previous theoretical studies. In contrast to the bulk phase, the spin-wave excitations in thin films are well defined in the whole two-dimensional Brillouin zone. It is shown that a non-magnetic substrate changes strongly both the dispersion and damping of the spin-waves.