A model-based wavefront sensorless (WFSless) adaptive optics (AO) system with a 61-element deformable mirror is simulated to correct the imaging of a turbulence-degraded extended object. A fast closed-loop control algorithm, which is based on the linear relation between the mean square of the aberration gradients and the second moment of the image intensity distribution, is used to generate the control signals for the actuators of the deformable mirror (DM). The restoration capability and the convergence rate of the AO system are investigated with different turbulence strength wave-front aberrations. Simulation results show the model-based WFSless AO system can restore those images degraded by different turbulence strengths successfully and obtain the correction very close to the achievable capability of the given DM. Compared with the ideal correction of 61-element DM, the averaged relative error of RMS value is 6%.The convergence rate of AO system is independent of the turbulence strength and only depends on the number of actuators of DM. © 2015 Optical Society of America.