A total of 139 long-period ground motion（GM） records are selected to study the effects of the parameters of restoring force models（restoring force models, stiffness ratio η，damping ratio ξ，displacement ductility ratio μ） and GM characteristics （period T，earthquake magnitude MW，site，PGA） on the input energy spectra SEI，hysteretic energy spectra SEH and damping energy spectra SED of the long-period GMs. Therefore, it can be found that: 1） there is a significant（slight） influence of the restoring force model on the long-period (conventional) seismic energy spectra, while there is a slight influence of the restoring force model on the conventional one; there is a slight influence of η on the long-period and conventional seismic energy spectra; with the increase of ξ，the spectral values in the long-period region of the long-period SEI increases, but for the conventional one it decreases; with the increase of μ，the peak platform and peak value of the long-period SEH is prolonged and decreases, but for the conventional one they are shortened and increases，respectively. 2）the larger MW results in the greater structural damage，while the softer site soil leads to the larger energy spectra value；the seismic energy spectra with other PGAoth can be obtained by multiplying the known seismic energy spectra with the reference PGAref by the equation of （PGAoth /PGAref）2. Then，based on the above parametric studies，the elastic long-period input energy design spectra are established by using a three-segment fitting function, and the influence formulas of μ and ξ on the long-period spectra are fitted. And then the inelastic long-period input energy design spectra are obtained.