The stochastic parallel gradient descent (SPGD) algorithm is a promising control algorithm for adaptive optics (AO) system without wave-front sensor. In this paper,a 61-element laser beam focusing AO system for correcting dynamical wave-front distortion was established,which used a hot-wind experimental atmospheric turbulence generator and SPGD algorithm controller based on field programmable gate array (FPGA). Up to one thousand iterations per second′s speed of the controller and the sub-millisecond response time of the deformable mirror and tilt mirror provided quick compensation for dynamic wave-front distortion induced by the hot-wind experimental atmospheric turbulence generator. The experimental results demonstrated that this AO system can significantly improve the laser beam quality with 30 times′ increase of the averaged performance metric and 10 times′ increase of the peak-values of far-field intensity distributions. The spectral analysis of performance metric showed that the AO system had an effective bandwidth of 10 Hz.