The analytical expression for the propagation of partially coherent flat-topped vortex beams through a paraxial optical ABCD system is derived and used to study the coherence vortex properties of partially coherent vortex beams in the focal region and free space. It is shown that the coherence vortex depends on the beam order N，spatial coherence parameter α and position (x1，y1) of the reference point. Depending on the choice of the reference point，the zero point of the spectral degree of coherence may be present or absent. In particular，if x1=y1=0 is chosen，the phase at the zero point of the spectral degree of coherence may be determinate，thus the coherence vortex does not exist.