Wavefront aberration occurs during laser propagating in the atmospheric turbulence, which reduces the performance of wireless optical communication system. We use a wavefront sensorless adaptive optics correction system based on the stochastic parallel gradient descent (SPGD) algorithm to correct the far field wavefront aberration. The simulation results indicate that the Strehl ratio of the proposed system is increased from 0.15 to 0.81, and the far field spot energy becomes converged. We take the intensity of the far field distorted spot detected by CCD camera as the objective function of the system, and experimentally verify the correction performances for different aberrations by the SPGD algorithm. After correction, the objective functions (the mean gray value of 900 pixels in the center) increase from 26.5 to 77.2, from 44.6 to 93.4, and from 110.6 to 208.5, respectively; the Strehl ratios increase from 0.23 to 0.67, from 0.39 to 0.75, and from 0.48 to 0.86, respectively. The central light intensity increases and the spot energy becomes converged. The experimental results are in good agreement with theoretical results.