Magnetorheological (MR) dampers exhibit a complex nonlinear hysteresis which makes the modeling of their behavior with parametric or non-parametric models to be challenging. In case of parametric models, the generalization of the parameters identified for a particular excitation is difficult and requires high computation costs. On the other hand, non-parametric models are considered as black-box type with no association to physical phenomena. The objective of this study is to propose a new identification model combining the merits of a parametric model and neural network paradigm. The proposed model is a parametric type which exploits an algebraic model with a hyperbolic tangent hysteresis, while a series multilayer-perceptron (MLP) neural networks are used to identify the model parameters under different excitation conditions. This approach not only preserves the physical meanings of the model parameters but also prompts generalization to common excitation conditions. The data for training the MLP neural networks were generated from a test program on a RD-8041-1 MR damper covering a wide range of input conditions. Results show that the proposed sequential neural network model not only increases the accuracy of the predicted MR damper force but also exhibits higher robustness and better consistency under different excitation conditions than a conventional algebraic model.