Based on light transfer matrix and electric field vector equation, the evolution of Airy beam propagating in periodic slab system with three negative index materials (NIMs) and its transmission mechanism are investigated. The intensity profiles on emergent surface of periodic slab system and side view of Airy beam propagating in each right handed material (RHM) and double negative material (DNM) unit including lossless and losses DNMs are discussed. It is revealed that the self-recovery Airy beam can be achieved in long distance by using lossless periodic slab system as long as the negative refractive index nl=-nr and each unit length L=Z. As to losses slab system contained DNMs, the smaller the collision frequencies are, the better the Airy beam quality is formed. It is expected that the proposed manner of beam transmission and corresponding conclusions can be useful for extension applications of optical control, especially for optical communication and optical encryption technique.