The main factors that affect ground motion include the earthquake source, the medium and path of seismic wave propagation and the local site condition. Although the spectral accelerations of ground motion have common characteristics in statistical sense, the specific shape of each acceleration record is unique, and some spectral accelerations have significant regular deviations from the statistical mean values. In this paper, based on the statistical analyses of 85976 sets of horizontal acceleration records obtained by Japanese KiK-net network, the statistical relationship of the PGA (peak ground acceleration) normalized spectral accelerations with magnitude and epicenter distance was obtained, and using 0.5 time of variances as the separatrix, and the acceleration records were divided into two categories, that is, the records with and without the regular deviations of spectral accelerations. By calculating the differences between the spectral accelerations of records with the regular deviations and the predicted spectral accelerations without the regular deviations, the regular deviations of the spectral accelerations were separated out, and the shapes of the regular deviations were verified to be highly consistent with the Gaussian curve. The regular deviations of spectral accelerations could be characterized by the central period, relative height and relative width of the regular deviations. Based on the statistical analyses of 25229 records with regular deviations of spectral accelerations, it was found that the characteristic parameters of regular deviations were mainly determined by local site conditions such as the shear wave velocity and the site property, and slightly affected by the earthquake magnitude, epicenter distance, ground motion intensity or other parameters. The empirical statistical relationships of the regular deviations were established using the multiple linear regression, and a method for determining the regular deviations of spectral accelerations was proposed. Although it needed to be improved, the concept of the regular deviations of spectral accelerations proposed in this paper would benefit the determining of site-related spectral accelerations of ground motion, and further contribute to the more reasonable ground motion input for engineering seismic design.