This paper presents a vehicle motion predictor for an autonomous racing system to assure safety when driving in limit handling situation. The proposed algorithm consists of two sequential parts; (1) Tire model identifier (2) Prediction of vehicle state. In the tire model identifier, parameters of a nonlinear tire model are identified through nonlinear optimization. In the prediction of vehicle sate, future vehicle states are calculated through numerical integration of a 2-DOF bicycle model that includes previously identified tire model. Moreover, assuming normal distribution of prediction error of each state, the probability of lateral instability and track escape of the future can be calculated. The proposed algorithm has been validated through computer simulations. The results show that the algorithm well predicts future vehicle states.