Abstract: Magnetorheological (MR) damper is a new kind shock absorption device of structure, which is affected by the applied magnetic field and temperature, etc. At present, many research efforts have been focused on performance test and mathematical model of MR damper, but the available models cannot capture the stiction phenomenon, inertial effect and temperature-rise effect during vibration. A temperature phenomenological model with mass element is proposed based on principle of fluid energy conservation. A numerical example is given in which the proposed mathematical model embodies not only the temperature's effect on MR damper but also the force-displacement and force-velocity nonlinear relationships of MR damper. The stiction phenomenon, inertial effect and the force roll-off in the low velocity region, are all well simulated.