Airy beam is a distinctive non-diffraction, which not only has properties of self -healing and non-diffraction, but also has the merit of self-bending that other non-diffraction beams do not have. The evolution of Airy beam′s non-diffraction, self-bending and self-healing was researched. The influence of different decay factor a and scale in the transverse x0 on the three characteristics of Airy beam was discussed. The research shows that the non-diffracting propagation distance of Airy beam will decrease with the increase of decay factor a when the scale in the transverse x0 is constant, and the decay factor has no impact on self-bending. It also manifests that the recovery distance of self-bending will decrease with the increase of decay factor a. When the decay factor a is constant, the distance of non-diffracting transmission, the offset of the self-bending as well as the healing distance of self-healing increases in proportion to the scale in the transverse x0. By comparing the effects of scale in the transverse x0 and decay factor a on the three characteristics of Airy beam, it is found that the influence of decay factor a on the three properties of Airy beam is smaller than that of scale in the transverse x0.