The propagation characteristics of Airy beam in the far-field were detailly studied, which start with the theoretical foundation, including the evolution process of intensity distribution, spot diameter and Power in the Bucket(PIB). The change regular of intensity distribution was investigated with the truncation factor a and the arbitrary scale in the transverse x₀ and how do a and x₀ influence the propagation Distance with Keeping Non-diffraction(DKNd), the Distance in which the Evolution became similar Guassian(DEG) and Self-bending Degree(SbD). The research shows that in the evolution process of intensity distribution which transforms into similar Guassian, the DKNd, DEG and SbD increase with the increase of x₀, the DKNd and DEG decrease with the increase of a and a has no effect on SbD. The evolution regular of spot diameter and PIB was also researched. The research shows that the spot diameter fistly remain unchanged and then increases, PIB firstly decreases, then increases and is 0.76 finally in the propagation progress under different values of a.