The atmosphere turbulence and imaging system noise can degrade and distort the imaging of the extended object. Adaptive optics technology is usually used to mitigate the wave-front aberrations caused by the atmosphere turbulence. An adaptive optics (AO) system with stochastic parallel gradient descent (SPGD) algorithm and a 61-element deformable mirror is simulated to restore the image of a turbulence-degraded extended object and the gray level variance function is used as the optimized object by controlling algorithm. Based on the above simulation mode, effects of imaging system noise on the correction capability of adaptive optics are discussed. The results show that the correct capability is not affected when the signal noise ratio (SNR) is bigger than 20 dB for relative small turbulence, while the correction capability becomes worse obviously as the SNR decreases. Under the same SNR, the stronger the turbulence, the bigger the effect on the correction capability.