A closed-loop control algorithm for sensorless adaptive optics system is proposed based on a relationship where the second moments of the wavefront gradients are approximately proportional to the modified far-field intensity distribution. An adaptive optics system simulation platform is established with a 61-element deformable mirror and a CCD imaging device. The convergence rate,the correction capability and the adaptability of the adaptive optics system are investigated through correcting wavefront aberrations under different strengths of turbulence. The results show that the model-based sensorless adaptive optics system can converge rapidly and obtain correction capability closing to the ideal correction of deformable mirror. The system only needs N+1 photodetector measurements when N order aberrations are corrected and the number of times of measuring far-field intensity is greatly reduced in comparison with existing control algorithms for sensorless adaptive optics system.