Published version of an article in the journal: Journal of Applied Mathematics. Also available from the publisher at: http://dx.doi.org/10.1155/2013/452391 Open Access ; Vehicle crash test is considered to be the most direct and common approach to assess the vehicle crashworthiness. However, it suffers from the drawbacks of high experiment cost and huge time consumption. Therefore, the establishment of a mathematical model of vehicle crash which can simplify the analysis process is significantly attractive. In this paper, we present the application of LPV-ARMAX model to simulate the car-to-pole collision with different initial impact velocities. The parameters of the LPV-ARMAX are assumed to have dependence on the initial impact velocities. Instead of establishing a set of LTI models for vehicle crashes with various impact velocities, the LPV-ARMAX model is comparatively simple and applicable to predict the responses of new collision situations different from the ones used for identification. Finally, the comparison between the predicted response and the real test data is conducted, which shows the high fidelity of the LPV-ARMAX model.