The phase singularity in optical field is an important subject in singular optics. Based on the generalized Huygens-Fresnel diffraction integral formula, the field distribution expressions and the phase singularity distribution expressions for anomalous hollow beams through an astigmatic lens are deduced, and used to study the phase singularities at the geometrical focal plane emphatically. The phase singularities may appear at the geometrical focal plane when the anomalous hollow beams pass through an astigmatic lens, and are dependent on the astigmatic coefficient and waist width. Under certain conditions, the ellipse or circular edge dislocations, optical vortices will appear at the geometrical focal plane. By changing the astigmatic coefficient or waist width, the ellipse or circular edge dislocations will vary, and the optical vortices will move, annihilate and appear.