A shared tuned mass damper (STMD) was proposed in previous research for reduction of dynamic responses of the adjacent buildings subjected to earthquake loads. A single STMD can provide similar control performance in comparison with two traditional TMDs. In previous research, a passive damper was used to connect the STMD with adjacent buildings. In this study, a smart magnetorheological (MR) damper was used instead of a passive damper to compose an adaptive smart STMD (ASTMD). Control performance of the ASTMD was investigated by numerical analyses. For this purpose, two 8-story buildings were used as example structures. Multi-input multi-output (MIMO) fuzzy logic controller (FLC) was used to control the command voltages sent to two MR dampers. The MIMO FLC was optimized by a multi-objective genetic algorithm. Numerical analyses showed that the ASTMD can effectively control dynamic responses of adjacent buildings subjected to earthquake excitations in comparison with a passive STMD.