In order to study the propagation characteristics of airy beams through negative index medium,the analytical expression was obtained for airy beams passing through the negative index medium based on the ABCD matrix optics theory.The propagation properties of airy beams passing through a negative index medium were obtained by using the formula.Numerical examples show that the intensity and the deflection position of the beam can be modulated by the frequency of the negative index medium.The deflection coefficient of the Airy beams is accelerate deflect as the frequency increases,different deflection position are obtained when the Airy beams propagating along z direction with different frequency.Both the deflection coefficient and the intensity of the Airy beam can be sensitively controlled by the frequency.The results show that it is convenient and efficient to modulate the Airy beam by the frequency of the negative index medium, the results presented in this paper may have some potential applications in optical device design and can be utilized in medicine science.