In order to study the modal intensity of partially coherent Airy vortex beams in the non-Kolmogorov turbulence, based on the generalized Huygens-Fresnel principle and the Rytov approximation theory, the analytical expressions of modal probability of partially coherent Airy vortex beams carrying orbital angular momentum were derived and the numerical simulation was carried out with MATLAB. The influence of turbulent parameters and beam parameters on the intensity of the vortex mode when partially coherent Airy vortex beams propagate in a non-Kolmogorov turbulence were investigated, the influence of the coherence width of partially coherent Airy vortex beams on the modal intensity during transmission was theoretically studied. The results indicate that partially coherent Airy vortex beams with a smaller topological charge, larger main ring radius and longer wavelength can effectively mitigate the influence of turbulence effect and reduce the crosstalk between modes in strong turbulence; larger non-Kolmogorov spectrum parameter and smaller detector aperture diameter can improve the modal intensity of partially coherent Airy vortex beams. Furthermore, compared with fully coherent vortex beams, partially coherent vortex beams have stronger turbulence resistance and better transmission performance in atmospheric turbulence. While poor coherence will lead to dispersion of spiral spectrum. The research results provide reference for the application of partially coherent Airy vortex beams in free space optical communication.