Over the past 10 years there has been a growing need to introduce closed-loop control technology for vibration suppression of buildings subject to wind or earthquake disturbances. This paper deals with the investigation of the effectiveness of a fuzzy logic based time variable damping tuned mass damper (TMD) on a building structure undergoing free and forced vibrations. The uniqueness of this approach is the application of a robust, nonlinear fuzzy based controller to emulate a time-optimal control strategy. Fuzzy logic based time variable damping is introduced into a semi-active TMD in order to enhance its performance in the vibration suppression of buildings. First, a single story structure for three different vibration suppression approaches is studied. The fuzzy logic based time variable damping TMD (fuzzy TMD) is compared to the baseline passive TMD as well as a conventional proportional-derivative (PD) controller. Forced vibration is introduced using a resonant harmonic sinusoidal excitation (i.e. same frequency as the fundamental frequency of the structure). Finally, the fuzzy TMD is compared to the baseline for the free vibration of a 15 story structure. For both structures studied, MATLAB based simulation results show that the passive TMD and the PD, both constant gain approaches, provide similar results whereas the fuzzy TMD yields half the settling time. This effort clearly demonstrates the potential of a variable gain (damping) strategy for the vibration suppression of buildings.