Measurements of the microwave surface impedance for high-temperature superconductor (HTS) YBa2Cu3O7-x(YBCO) films irradiated by 3 MeV Au2+ ions at three irradiation doses (1010cm-2, 1011cm-2, and 1012cm-2) were carried out at different temperatures (below the critical temperature Тс∼90К) and various rf current amplitudes by use of microstrip resonator technique. Noticeable decrease of the surface resistance and enhancement of the linear response range at low temperatures were observed for moderately irradiated film exposed to irradiation dose 1011cm-2, while at higher irradiation doses (1012cm-2) increase of the surface resistance and decrease of the linear response range were observed for all temperatures below Tc. These results are discussed in the framework of phenomenological theory for microwave response of superconductors with nano-sized structural defects.