Tuned mass dampers (TMDs) are a combination of mass, spring, and damper that are added to a structure to reduce its response to lateral excitation, such as wind forces and earthquake excitation, especially in the displacement range. Due to the very rich frequency content of earthquake excitation, the use of TMDs in steel moment frames does not necessarily improve the structural behavior under all earthquake excitations. Exclamation The time-history method is a new nonlinear dynamic method for estimating the behavior of structures under earthquake excitation. In this analysis method, the structure is subjected to an artificial incremental excitation. The results of the nonlinear time history analysis show that the TMD reduces the average maximum roof displacement under selected ground motion records. The performance of the TMD also improves with increasing mass ratio and increasing building height. Adding a TMD to steel moment frames reduces the average maximum roof acceleration under selected ground motion records and also reduces the average maximum base shear of the building. The time-history method estimation of the maximum roof displacements of the structure at a hazard level equivalent to a 475-year return period earthquake is also 10% to 20% less than the nonlinear time-history method. Exclamation The time-history method estimation of the maximum roof acceleration of the structure at a hazard level equivalent to a 475-year return period earthquake is also 10% to 20% more than the nonlinear time-history method. Exclamation The time-history method estimation of the maximum base shear of the structure at the considered hazard level is also 5% to 15% more than the nonlinear time-history method.