Thus far, focusing a single beam and combining multi-optical Gaussian beams have become two major methods of locally enhancing output laser intensity. In this paper, we propose a method of generating free space auto-focusing beams by combining multiple one-dimensional Airy beams. By employing split-step beam propagation method, auto-focusing beams generated by four and eight one-dimensional Airy beams are numerically simulated, and their intensity distributions are displayed from both transverse plane and side-view propagation. By utilizing a spatial light modulator and computer generated phase masks, these auto-focusing beams are experimentally demonstrated. Our experimental results accord well with the numerical simulations.