Profile of a dark hollow beam in sub-diffraction -limit imaging is of crucial importance for its spatial resolution when using the coherent anti-Stokes Raman scattering microscopy, as far as the imaging quality is concerned. Therefore, the generation of dark hollow beams through a vortex phase plate will be theoretically analyzed based on the Fresnel diffraction theory. Influences of different incidence conditions on the intensity distribution of the generated dark hollow beams are also investigated. And it is shown that a perfect dark hollow beam could be produced when a Gaussian beam is vertically incident upon a first-order vortex phase plate, with the incident light wavelength equal to that of the phase plate. However, both the circular symmetry of the incident beam's intensity distribution and the alignment between the centers of Gaussian beam and phase plate may affect the intensity distribution of the dark hollow beam, which will almost be in circular symmetry though it may shift some distance from the image center when at a small incident angle. Furthermore, the dark hollow beam's intensity distribution will scarcely change when the central wavelength deviation is very small from the incidence light and the phase plate. These results may be of great value in generation of perfect dark hollow beams in sub-diffraction –limit imaging by coherent anti-Stokes Raman scattering microscopy.