A model for a Magneto-Rheological (MR) damper based on Artificial Neural Networks (ANN) is proposed. The design of the ANN model is focused to get the best architecture that manages the trade-off between computing cost and performance. Experimental data provided from two MR dampers with different properties have been used to validate the performance of the proposed ANN model in comparison with the classical parametric model of Bingham. Based on the RMSE index, an average error of 7.2% is obtained by the ANN model, by taking into account 5 experiments with 10 replicas each one; while the Bingham model has 13.8% of error. Both model structures were used in a suspension control system for a Quarter of Vehicle (QoV) model in order to evaluate the effect of its accuracy into the design/evaluation of the control system. Simulation results show that the accurate ANN-based damper model fulfills with the control goals; while the Bingham model does not fulfill them, by concluding erroneously that the controller is insufficient and must be redesigned. The accurate MR damper model validates a realistic QoV model response compliance.