In recent years，several disastrous near fault earthquakes，such as the Wenchuan earthquake in China，the Chi Chi earthquake in Taiwan，the Kobe earthquake in Japan，and the Northridge earthquake in the United States，have occurred.A large amount of near-fault pulse-type earthquake data from all these earthquakes has been recorded，and has attracted close scrutiny and extensive research.This seismic record contains obvious long period velocity pulses.Near-fault ground motions not only cause serious damage to buildings，but also cause slope instability and damage to infrastructure，These disasters have a serious impact on the economic infrastructure and safety of people.Therefore，understanding the response of structures to near-fault ground motions is necessary.This allows for more reliable and efficient seismic design.Different ground motion records contain different types of information such as peak acceleration，peak velocity，peak displacement，and duration of ground motions.Near-fault ground motions have prominent features and destructive force and their velocity response spectra are significantly different from the velocity response spectra of far-fault ground motions.This study used 30 near-fault earthquake records from the Pacific Earthquake Engineering Research Center’s strong motion database；the records contain magnitude，fault mechanism，soil layer shear wave velocity，and fault distance information.First，a motion equation for a single degree-of-freedom system was established.Then，a state-space method and MATLAB was used to change the motion equation to a state equation.Next the equation was solved to obtain the velocity response of a single degree-of-freedom system and based on the velocity response，the velocity response spectra of the single degree-of-freedom system was obtained.Because the velocity response is related to the acceleration response and the displacement response，the velocity response of structures are analyzed in the present study.The features of the velocity response spectra were obtained by normalizing and averaging，and then the 30 near-fault earthquake records selected from the PEER strong motion database were divided into different groups based on the period corresponding to the peak velocity.A velocity design spectra was established using a piecewise linear fitting method.The reasonableness of the velocity design spectra was verified by comparing the velocity design spectra and the velocity average spectra of different groups.The results show that the velocity response spectra of near-fault ground motions consist of four stages：ascent segment，peak segment，depression segment，and horizontal segment.The damping ratio of the structure has no influence on the spectral shape of the velocity response spectra，but the damping ratio of the structure can affect the spectra peak of the velocity response spectra.When the damping ratio of the structure is different，the maximum relative error of the velocity response spectra peak is 16.68% after pairwise comparison.