The Shack–Hartmann wavefront sensor (SHWFS) traditionally employs the center of gravity (CoG), windowing, and thresholding CoG (TCoG) algorithms to measure wavefront aberrations. Nevertheless, these algorithms yield low accuracy in a low signal-to-noise ratio (SNR) environment, and therefore, we propose a measurement algorithm based on the Kalman filter to correct the three algorithms’ centroid position of the Shack–Hartmann spot. When the Euclidean distance between the reference centroid in a sub-aperture and the measurement centroid exceeds a certain threshold, the sub-apertures centroid position is untrusted and must be corrected. Several simulation experiments are conducted in three environments: no noise, Poisson noise, and Gaussian noise; they demonstrate that the proposed algorithm effectively improves the centroid’s accuracy by more than 10% and ensures real-time performance for the adaptive optics system. In addition, experimental results on wavefront reconstruction tasks reveal that our algorithm produces wavefronts close to the original.