Recently, a number of researches about linear magnetorheological(MR) damper using valve-mode characteristics of MR fluid have sufficiently undertaken, but researches about rotary MR damper using shear-mode characteristics of MR fluid are not enough. In this paper, we performed vibration control of shear-mode MR damper for unlimited rotating actuator of mobile robot. Also fuzzy logic based vibration control for shear-mode MR damper is suggested. The parameters, like scaling factor of input/output and center of the triangular membership functions associated with the different linguistic variables, are tuned by genetic algorithm. Simulation results demonstrate the effectiveness of the fuzzy-skyhook controller for vibration control of shear-mode MR damper under impact force.