The mixing process of three narrow line-width laser beams with different wavelengths in the sample is analyzed with semi-classical theory and a set of coupling-wave equations for describing the generation process of coherent anti-Stokes Raman Scattering (CARS) signals is derived. Based on the derived CARS coupling-wave equations and the principle of the time-resolved method,a set of coupling-wave equations for describing the time-resolved CARS (T-CARS) method is obtained. The variation of CARS signals and non-resonant background noise with incident laser beams in the T-CARS method and the decaying process of molecular vibrations have been investigated by numerical simulation. The decaying time of molecular vibrations can be used to distinguish different molecules with similar components and structure,and monitor the change of microenvironment. Theoretical study of T-CARS method using narrow line-width laser source shows that whole Raman spectra of biomolecules can be obtained by using wide-spectrum laser source.