In this paper, an aberration correction algorithm for wavefront sensorless adaptive optics system is presented, which is based on the approximately linear relation between the mean square of the aberration gradients and the second moment of far-field intensity distribution. To demonstrate algorithm's performance, an experiment system of aberration corrections for Fresnel zone plates imaging is set up. The correction results show the excellent performance of this method in correction speed, and correction capability. Comparing with conventional stochastic parallel gradient descent (SPGD) algorithm, the correction speed with this method is improved about four times for the similar correction effect.