In order to study the propagation characteristics of the polarization singularity based on the fractional vortex beam in free space, the method of numerical simulation was adopted, the theoretical analysis and data simulation were carried out, and the evolution of topology of polarization singularity based on the fractional circular Airy vortex beam was obtained during propagation in free space. The results show that regardless of whether there is a circular polarization singularity in the initial plane, the self-focusing properties of the polarization singularity based on the fractional circular Airy vortex beam will affect the topology of the light field during the propagation process, making the light field doesn’t contain circular polarization singularities at the beginning of transmission, but after traveling through its self-focusing distance, several circular polarization singularities will appear in the light field. Compared with polarization singularities based on integer circular Airy vortex beams, both have singular topology self-recovery properties, while fractional-based vortex beams will bring more circular polarization singularities into the recovered light field point. This work will deepen the understanding of the propagation characteristics of polarization singularities, provide a theoretical basis for its application, and broaden the application range of circular Airy beams.