By using Huygens-Fresnel diffraction integral formula and the transfer matrix method, the analytical expression of radially and azimuthally polarized chirped Airy-Gaussian vortex beams through left-handed materials and right-handed materials can be obtained. We study the effects of the chirp factor and the distribution factor on the radially and azimuthally polarized chirped Airy-Gaussian vortex beams in the propagation process, including the light intensity, the phase distribution, the propagation path, the peak intensity, and the radiation force. The focal position of the beams can be adjusted by the chirp parameter.