Described by the fractional Schrödinger equation (FSE) with the parabolic potential, the periodic evolution of the astigmatic chirped symmetric Pearcey Gaussian vortex beams (SPGVBs) is exhibited numerically and some interesting behaviors are found. The beams show stable oscillation and autofocus effect periodically during the propagation for a larger Lévy index (0 < α ≤ 2). With the augment of the α, the focal intensity is enhanced and the focal length becomes shorter when 0 < α ≤ 1. However, for a larger α, the autofocusing effect gets weaker, and the focal length monotonously reduces, when 1 < α ≤ 2. Moreover, the symmetry of the intensity distribution, the shape of the light spot and the focal length of the beams can be controlled by the second-order chirped factor, the potential depth, as well as the order of the topological charge. Finally, the Poynting vector and the angular momentum of the beams prove the autofocusing and diffraction behaviors. These unique properties open more opportunities of developing applications to optical switch and optical manipulation.