Laser beam wandering induced by air turbulence could be crucial for applications such as free-space optical communications, LIDAR, and remote air lasing. In this study, the influence of air turbulence on the transverse wandering of a Gauss laser beam with and without an axicon as the focusing optical component has been investigated. It has been demonstrated that the turbulence-induced beam wandering could be dramatically suppressed by using an axicon. Further, the corresponding mechanism has been discussed. This work would bring great benefits to many practical applications relying on a stable laser beam in a turbulent atmosphere.