Star centroid systematic error is called pixel frequency error, whose period is the width of the pixel. The analysis of the distribution of systematic error is useful in error compensation. Point spread function is the main factor which affects the distribution of systematic error. Traditionally the Gauss point spread function is used in the frequency analysis of the systematic error, but its reasonability has not been taken into consideration. With real star image considered, the Giancarlo point spread function was compared with the Gauss point spread function. Then the Giancarlo point spread function was used in the spacial frequency analysis of star centroid systematic error, and the theoretical formulas of the systematic error was obtained. Compared with the result of the traditional frequency analysis, an item that modulated the amplitude of the S curve distribution was added to the theoretical formulas, and that made the x coordinate systematic error distributed as an S curve along x axis and the amplitude of S curve changed along y axis. A simulation under a condition with noise was carried out, and the result was in accordance with the frequency analysis of this article. Finally an experiment is done, the result of the experiment is compensated for according to the theoretical formulas, the star centroid accuracy is improved by 54.42%, which is better than the traditional sine curve fitting compensation method.