Semi-active control of civil engineering structures has been widely implemented as they incorporate the inherent reliability of passive control systems and versatility to adapt as of active control systems. One such semi-active system is the usage of Magnetorheological (MR) damper in the control strategy. This paper presents the use of MR damper on a single degree of freedom (SDOF) system, modelled using the SIMULINK toolbox of MATLAB. The modified Bouc-Wen hysteretic model is used to model the MR damper. The developed SIMULINK model of the MR damper is validated with the experimental results available in the literature. A parametric study has been carried out to understand the effect of period on the response of the SDOF system with MR damper. In order to study the influence of uncertainties on system response, the fuzzy logic control algorithm is incorporated in the SDOF system with MR damper. It is found that the fuzzy controller reduces the voltage requirement of the MR damper by 80% as compared to that of the MR damper in passive on condition.