Abstract: Due to the limitation in the installation space in real engineering structures, it is necessary to restrict the stroke of Tuning Mass Damper (TMD) to prevent the severe impact between TMD and structure walls. For the TMD moving in a lower speed, the restoration force of impact can be simulated by Hertz model. The nonlinear equations of two degree freedom system are derived, and then the equations are simplified into the non-dimensional equations. The reducing effect is investigated, which depends on many impact parameters, such as clearance ratio, frequency ratio and mass ratio etc.; and the time history of impact force is also reconstructed. The numerical results show that the dimensionless clearance ratio and frequency ratio are more sensitive parameters. The optimum clearance ratio exists when other parameters are fixed. The dynamic response of main structure can be effectively reduced and the robustness of TMD can be improved significantly with respect to the change of structural parameters, if the impact parameters are reasonably designed.