The wavefront sensorless adaptive optics (WFSless AO) system under noise is established using an 88-element deformable mirror and a charge coupled device imaging device and with an extended object as a correction object. The linear relationship between the masked detector signal and the mean-square wavefront gradient of the extended object imaging under noise is verified. The algorithm based on this linear relationship is used as the control algorithm of the WFSless AO system. The simulation experiment is carried out to check the correction ability of the model-based WFSless AO system for extended object imaging under noise. The results show that the correction effects are very close under the same turbulence condition but different signal-to-noise ratios. According to the order of turbulence conditions from small to large, the averaged root mean square relative errors after correction under a signal-to-noise ratio of 5 dB are 3.71%, 2.94% and 2.42%, respectively, if compared with the results under a signal-to-noise ratio of 20 dB. The above results indicate that the model-based control algorithm with this linear relationship has a relatively good anti-noise capability.