The analytical expression for the propagation of flat-topped vortex beam through an aperture paraxial optical ABCD system is derived. Taking aperture lens and rectangular aperture as typical examples, evolution of phase singularities between flat-topped vortex beam and flat-topped beam is comparatively studied. The effect of the aperture truncation, relative off-axis displacement and beam order on evolution of phase singularities is illustrated by numerical examples. The results show that there always exists phase singularities for flat-topped vortex beam through an aperture, and the phase singularities take place in the diffracted field even the vortex core is stopped by the aperture. However, numerical calculations show that edge dislocations appear for flat-topped beam through aperture lens, and the evolution and annihilation of the edge dislocations take place with increasing of truncation parameter, while the phase singularities are not found for flat-topped beam through rectangular aperture.