Based on light transfer matrix and generalized Huygens-Fresnel optical diffraction formula, the propagation evolution of Airy Gaussian vortex beam's normalized intensity distribution on emergent surface, side transmission view in periodic slab system contained right-handed and double negative material(DNM) were explored. Research shows that the original Airy Gaussian vortex beam intensity can be restored immaculately by using periodic slab system contained negative index material as long as the negative refractive index abs(nl)=nr and each unit length R:L=1:1; while abs(nl)≠nr but R=L, both types of emerging beams had poor quality, and in order to achieve beam reconstruction, the larger abs(nl) was, the longer DNM unit length was needed, and vice versa. Relation between DNM unit length and nl was thoroughly studied as well. It is expected that the relevant conclusions could provide important reference value for extension applications of optical control and communication transmission technique of the Airy Gaussian vortex beam propagating in the periodic and quasi-periodic metamaterials structure.