Simulated star maps serve as convenient inputs for the test of a star sensor, whose standardability mostly depends on the centroid precision of the simulated star image, so it is necessary to accomplish systematic error compensation for the simple Gaussian PSF (or SPSF, in which PSF denotes point spread function). Firstly, the error mechanism of the SPSF is described, the reason of centroid deviations of the simulated star images based on SPSF lies in the unreasonable sampling positions (the centers of the covered pixels) of the Gaussian probability density function. Then in reference to the IPSF simulated star image spots regarded as ideal ones, and by means of normalization and numerical fitting, the pixel center offset function expressions are got, so the systematic centroid error compensation can be executed simply by substituting the pixel central position with the offset position in the SPSF. Finally, the centroid precision tests are conducted for the three big error cases of Gaussian radius σ = 0.5, 0.6, 0.671 pixel, and the centroid accuracy with the compensated SPSF (when σ = 0.5) is improved to 2.83 times that of the primitive SPSF, reaching a 0.008 pixel error, an equivalent level of the IPSF. Besides its simplicity, the compensated SPSF further increases both the shape similarity and the centroid precision of simulated star images, which helps to improve the image quality and the standardability of the outputs of an electronic star map simulator (ESS).