To realize the accurate control of magneto-rheological system, the nonlinear dynamic model as the joint of damper and control strategy is worthy of being investigated. In this study, the modeling methods based on the backbone curve are proposed to portray the dynamic characteristics of magneto-rheological damper. The modeling methods contain the phase lag method and the hysteresis division method. Six novel algebraic models are deduced from the two methods and compared systematically. The parameters identification of models is conducted by the nonlinear least square method. The nonlinear least square optimization problem is solved by the Levenberg–Marquardt algorithm. The evaluation indexes including the root-mean-square error, mean deviation and computation time are calculated to evaluate the accuracy and feasibility of the novel models. Results show that the modeling methods and their models can describe the nonlinear hysteretic characteristics with feasibility and accuracy.