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The recent advances in vehicle industry and vehicle-to-everything communications are creating a huge potential market of intelligent vehicle applications, and exploiting vehicle mobility is of great importance in this field. Hence, this paper proposes a novel vehicle mobility prediction algorithm to support intelligent vehicle applications. First, a theoretical analysis is given to quantitatively reveal the predictability of vehicle mobility. Based on the knowledge earned from theoretical analysis, a deep recurrent neural network (RNN)-based algorithm called DeepVM is proposed to predict vehicle mobility in a future period of several or tens of minutes. Comprehensive evaluations have been carried out based on the real taxi mobility data in Tokyo, Japan. The results have not only proved the correctness of our theoretical analysis, but also validated that DeepVM can significantly improve the quality of vehicle mobility prediction compared with other state-of-art algorithms.