The numerical model of correlation wave-front sensing algorithm (COR) based adaptive optics (AO) system was established. Collimated uplink propagation beam corrected by AO was numerically simulated. The influence of photon noise and read-out noise on AO correction efficiency under different thermal blooming strength was analyzed, and compared with the results based on center of gravity(COG) algorithm and threshold center of gravity(TCOG) algorithm. The results show that the COR which is more robust to variety of the noise strength and thermal blooming strength, can improve the wave-front sensing precision of the Shack-Hartmann wave-front sensor(SH-WFS) under low signal-to-noise ratio (SNR) circumstance and restrain the phase compensation instability (PCI) induced by noise either, which will improve the AO correction efficiency and stability under low SNR circumstances.