Based on the generalized Huygens-Fresnel diffraction integral formula, field distribution expression of sinh-Gaussian beams passing through astigmatic lens is derived. The intensity distribution and the phase characteristic of sinh-Gaussian beam on focal plane or near focal plane of astigmatic lens are numerically calculated. Theoretical analysis and numerical calculation results indicate that the appropriate beam parameters and astigmatic lens structure parameters can make sinh-Gaussian beam passing through astigmatic lens transform into dark hollow beam with vortex. Its topological charge index is 1. Besides, the beam parameters and the lens coefficients affecting the field intensity distribution and phase distribution are discussed. It is found that the astigmatism of lens plays a critical role in converting sinh-Gaussian beam into a dark hollow beam with vortex through focusing of astigmatism lens, and a super-long dark hollow beam can be obtained with the astigmatic lens.