A common situation found in many old and modern buildings is the annoying floor vibration. Many old buildings suffer floor vibration as no specific design guidelines were employed to limit the situation. In modern buildings, the development of floors of lighter weight, longer span, and less inherent damping is the main cause for the annoying vibration. In this paper, as a novel application, the influence of viscoelastic tuned mass dampers (TMDs) in vibration mitigation of an existing steel joist jack arch floor structure is investigated using finite element (FE) analysis. Results of a free vibration test conducted on the prototype TMDs are used to validate the FE model. The jack arch floor is subjected to the walking loads of different stepping rates of 1.5, 2, and 3 Hz. Various load models that are available in the literature are used to define the dynamic walking load, and the response mitigation is carried out based on the most critical load models. The influence of design parameters such as the excitation frequency, configuration of the individual dampers in the TMD system, and the mass ratio of the TMD system on the vibration mitigation of the floor structure are investigated in detail. Results of this study indicate that the viscoelastic TMDs are effective in vibration mitigation of jack arch floor structures.