We introduce the circle Pearcey Gaussian vortex (CPGV) beams in a harmonic potential for the first time and investigate their abruptly autofocusing properties by theoretical analysis and numerical simulations in this paper. By varying the spatial distribution factors, one can effectively control the propagating dynamics of the beams, including the position of the focus, the radius of the focal light spot and the intensity contrast. Meanwhile, the magnitude of topological charges and the position of the vortex can alter the focal pattern and the intensity contrast. Furthermore, the position of the focus can be flexibly controlled in a tiny range by adjusting the scaled parameter of the incident beam properly.