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We present an investigation on the propagation properties of the chirped Airy vortex (CAiV) beams through slabs of left-handed materials (LHMs) and right-handed materials (RHMs). We discuss the influence of chirped parameter C on the propagation of the CAiV beams through LHM and RHM slabs. Our simulation results show that a maximum accelerated velocity appears during the propagation process. The intensity concentration of the CAiV beams increases with the absolute value of the chirped parameter. The peak intensity of the CAiV beams changes abruptly, and the chirped parameter plays an active role on the difference of the maximum and the minimum. In the energy flow, we find that the effects of the chirped parameter on the strength of the vortex are different at different propagation distances.