Near-fault velocity pulse ground motion records are characterized by large amplitude and long pulse period, which tend to cause significant damage to engineering structures. This study selects 107 near-fault station horizontal velocity pulse-like records of 16 seismic events. The records are classified into 6 types. The multi-damping ratio acceleration response spectra are calibrated using the differential evolution algorithm. The differences between the calibrated spectra of different types of residual records and the original records are compared. The variation trends of the calibrated spectra parameters with damping ratio are analyzed. The conclusions are as follows: In the short-period range, the calibrated spectra of the original records are similar to those of the residual records. In the long-period range, the calibrated spectra of the original records are significantly larger than those of the residual records. The average βmax and γ of different faults and velocity pulse types decrease with the increase of damping ratio. The average Tg of the calibrated spectra of the original records is greater than that of the corresponding residual records. The average βmax values of the original records and the residual records are similar. The average γ of the calibrated spectra of the residual records is greater than that of the original records.