For an N-element deformable mirror, the model-based wavefront sensorless adaptive optics (AO) system only needs N+1 imaging acquisitions, which means rapid convergence. An AO system was simulated with an 88-element deformable mirror and a CCD. The convergence and the correction performance of AO system under noise were investigated. Results showed that the convergence under noise is the same as that of AO system under no noise. The correction effect is very close to each other under different noise for the same turbulence condition. Compared with correction results under 50 dB, averaged RMS relative errors of 30 dB are 4.75%, 4.04% and 2.58% respectively according to given turbulence conditions from weak to strong. Above results verified that the model-based wavefront sensorless AO system has a relative strong anti-noise capability.江苏省高校自然科学基金(14KJB510004)