Neural networks system identification have been widely used for estimate the nonlinear model of system. In this paper, multilayer perceptron neural network is used for identifying the Nonlinear AutoRegressive with eXogenous input (NARX) model of a quarter car passive suspension system. Input output data are acquired by driving a car on a special road event. The networks structure is developed based on system model. The Networks learning algorithm is derived using Fisher's scoring method. Then the Fisher information is given as a weighted covariance matrix of inputs and outputs the network hidden layer. Unitwise Fisher's scoring method reduces to the algorithm in which each unit estimate its own weights by a weighted least square method. The results show that the method uses suitable for modeling a quarter car passive suspension systems.