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A new dynamic tire model for estimating the longitudinal/lateral road-tire friction force was derived in this paper. The model was based on the previous Dugoff tire model, in consideration of its drawback that it does not reflect the actual change trend that the tire friction force decreases with the increment of wheel slip ratio when it enters into the nonlinear region. The Dugoff model was modified by fitting a series of tire force data and compared with the commonly used Magic Formula model. This new dynamic friction model is able to capture accurately the transient behavior of the friction force observed during pure longitudinal wheel slip, lateral sideslip and combined slip situation. Simulation has been done under different situations, while the results validate the accuracy of the new tire friction model in predicting tire/road friction force during transient vehicle motion.