In this paper a modified parametric algebraic model was proposed to capture the hysteretic behaviour of the Magneto-rheological (MR) damper. The superiority of the proposed modified model was shown by comparing it with the algebraic model. It is observed that although two models are comparable at lower voltage inputs of 1V, 2V and 3V the modified algebraic model is remarkably successful at higher voltage inputs of 5V and 7V at the highest excitation velocity of 200m/s over the algebraic model. Apart from its accuracy, modified algebraic model is also more preferable in terms of its low computational expenses compared to differential modified Bouc-Wen?s model which is highly computationally demanding. Therefore it was concluded that the proposed modified algebraic model can be used to develop more effective control algorithms for such devices.