Daytime use of Shack-Hartmann wavefront sensor (SHWS)-based adaptive optics (AO) at a telescope is hindered by the fluctuating bright sky background. Therefore, we propose a Gaussian modeling centroid extraction algorithm that performs real-time daylight AO closed-loop corrections. The algorithm is executed in the process of modeling and updating each pixel of the consecutive SHWS images. The simulation results show that our method can provide a lower centroid estimation error (CEE) for bright sky background conditions. We also performed a field experiment on a 2 m ground-based telescope and achieved a daylight AO correction of 2.1 times diffraction limit for a star with a visual magnitude of 4.7 (HIP113116) when the elevation angle of the sun was 7.7°. This represents the first publicly reported daylight natural guide star AO correction result on a 2 m class telescope.