In rotating machinery, unattenuated excessive torsional vibration leads to damage and excessive wear. This type of vibration, which is transferred from one structure to another can be estimated using torsional transmissibility factor (TTF). The value of the TTF describes the ratio of output to input and reaches its peak at the natural frequency. Hence, the ability to vary coupling stiffness of two rotating shafts will allow the control of the TTF towards better performance and preventions from fatigue loading. Traditionally, passive rubbers are used as a flexible coupling in between two shafts. However, the constant passive stiffness of the material limits its performance. To address this issue, an adaptive coupling based on magnetorheological elastomer (MRE) is proposed to achieve better TTF at varying frequencies. Mathematical modelling, simulation study and experimental results of MRE for torsional vibration isolation are presented in this work. Natural frequency obtained from the TTF shows an increase of about 3 Hz when current changed from 1 to 6 A.