Floor vibration due to human activities is becoming a significant concern to designers and developers of long span lightweight floor systems. Modern office floors are now constructed with longer spans and lighter structural members. Actual office dead loads and floor damping are significantly lower than what they were in the past, increasing the potential for annoying floor vibration. Traditional techniques to reduce vibrations through structural modifications have some serious shortcomings, especially with existing structures. This paper discusses the development of an innovative configuration for a tuned mass damper (TMD) using viscoelastic material in rectifying problematic floors. General analytical formulae to predict the response of a floor fitted with multiple identical TMDs are developed. Experimental and numerical studies on the performance of a custom-made distributed multiple viscoelastic TMD system in suppressing the vibration level on an actual office floor subjected to various types of excitations are discussed. The effects of the damper location, the variation in the floor and/or dampers dynamic characteristics on the effectiveness of this control approach have been taken into account. The installed damper system has successfully suppressed the floor response level to an acceptable limit for human comfort, in the case study presented.