In Shack-Hartmann wavefront sensor(SH-WFS) based adaptive optics system, the centroiding algorithm is usually used to estimate the centroid of a point source spot. But the detecting accuracy of the centroiding algorithm is affected by many factors such as threshold selection, so that the centroid position of the spot cannot be evaluated accurataly under the condition of low signal-to-noise ratio(SNR) . Comparatively the correlating algorithm for Shack-Hartmann wave front-sensing is more robust because it need not reduce the thresholding. In this paper, based on the the principle of the correlating SH-WFS, the measurement error of the correlating SH-WFS is derived by building up the noise model of the correlating SH-WFS. The influences of spot size, photon noise, read out noise and background light noise on the measurement of the correlating SH-WFS are analyzed systematically. The numerically simulation results and the experimental results are consistent well with the theoretical analyses.