The interactions between a two-level atom and a coherent field with a time-varying frequency without rotating-wave approximation have been investigated. The typical cases of the frequency of the field varying with time in the sine and rectangle forms have been considered. It is found that the collapse-revival phenomena and quick oscillations due to virtual photon processes of the atomic population inversion are deformed as the frequency changes with time in the sine form. The rectangular frequency modulation can lead to some new collapses and revivals in the evolution of the atomic population inversion. The sudden jumping of the field frequency can also lead to the sudden change of the quick oscillations due to virtual photon processes.