The resonance effect of special long-period ground motions to (super) high-rise buildings is significant, which is likely to cause serious damage to these long-period structures. Therefore, the influence of long-period ground motions cannot be ignored in the seismic design of long-period structures. To provide theoretical basis and quantitative criteria for the selection and evaluation of long-period ground motion records, a quantitative bounded method based on the normalized acceleration spectra is proposed. Firstly, two types of long-period ground motions with reliable information are selected for this research, and the baseline drifting on acceleration, velocity and displacement time-history curve are corrected. Then, the Fourier amplitude spectrum and Power spectral density amplitude of special long-period ground motions are analyzed. Lastly, a quantitative boundary parameter to distinguish near-fault pulse-like (NFPL) and far-field harmonic (FFH) ground motions from common ground motions are discussed. Study results are obtained as follows: The frequency distribution of special long-period ground motions is relatively concentrated in low-frequency band, and the frequency distribution of common ground motions is relatively dispersed in medium-high-frequency band. Power spectral density amplitude and Fourier amplitude spectrum are the specific performance of energy distribution about earthquake records from the aspect of frequency domain, and they have no interrelation with structural seismic response under earthquake excitation. The specific earthquake records whose weighted average value of acceleration amplification factor is less than 0.2 are known as common ground motions. The specific earthquake records whose weighted average value is between in 0.2~0.6 are known as NFPL ground motions. The specific earthquake records whose weighted average value is beyond 0.6 are known as FFH ground motions. It would provide reference for the selection of long-period ground motions during seismic analysis of long-period such as super high-rise building structures.