The constant-ductility seismic demand spectra can provide high-sight of seismic damage mechanism of inelastic structures under the earthquake. And in the displacement-based seismic design, the constant-ductility seismic demand spectra are very useful for the preliminary design of new structures where the global displacement ductility capacity is known, which can provide the required inelastic lateral strength of new structures from the required elastic lateral strength. An in-depth investigation of damping effect on constant-ductility seismic demand spectra of inelastic structures is presented in this paper. A statistical study is performed of inelastic response computed for different damping ratio SDOF systems with different levels of lateral yielding strength required to maintain the given displacement ductility when subjected to a large number earthquake accelerations. It is concluded that the damping effect on constant-ductility seismic resistance spectra is rather complex. It depends on not only site conditions but also the structural period. Finally, results from non-linear regression analysis are presented that provide a simplified expression to be used to approximately quantify the damping effect.