Based on light transfer matrix and Collins integral equation, the evolution of Airy Gaussian beam intensity side view in double negative material (DNM) with and without loss was discussed. Results show that the renewed original Airy Gaussian beam can be achieved perfectly by using lossless slab system contained negative index material as long as the negative refractive index nl=-nr and DNM unit length equals to the sum of two RHM units length on both sides of DNM unit; while nl≠-nr, the larger abs(nl) is, the longer DNM is needed to achieve beam reconstruction,and vice versa. As to losses situation, the smaller collision factors are, the better output Airy Gaussian beam quality is formed. It is further explored the propagation properties of Airy Gaussian beam changed with ζ factor and exponential truncation factor a, it is found that the beam self-bend is more obvious, and main lobe and side lobes are multiple decreased with the smaller ζ, even though the intrinsic nature of Airy Gaussian beam can not be affected by ζ factor. The exponential truncation factor a can control Airy Gaussian beam’s outline that likes an Airy beam when a＜0.2, but transforms into Gaussian beam profile while a=0.7.