Magnetorheological (MR) dampers have received remarkable attention due to being a potential technology to conduct semi-active control in mechanical systems in order to effectively suppress vibration. It is therefore important to understand the dynamic behaviour of such devices whose non-linear hysteresis is a complicated phenomenon. In the study, an MR damper has been designed, fabricated, tested and then its dynamic behaviour has been modelled with the classical Bouc-Wen hysteretic model. After that, the seven parameters of this model have been expressed in terms of only current excitation. By this, the total damping force has been given by a compact form in which the only independent variable is the current excitation. Finally, the model has been verified with experimental data and a good agreement has been observed.