Vehicle-to-everything (V2X) communications have a great potential of enabling future intelligent vehicle applications, and exploiting vehicle mobility is of great importance in designing efficient V2X protocols and applications. Thus, this paper proposes a novel edge-assisted algorithm that makes use of the resources in both cloud and edge sides of vehicular networks to predict vehicle mobility. The proposed algorithm adopts a hybrid architecture of convolutional and recurrent neural networks, and enables computationally efficient transfer learning in each vehicle to generate its customized mobility prediction model. Extensive evaluations have been conducted by using a real taxi mobility data set that is obtained from a testbed deployed in Tokyo, Japan. The results have validated that, compared with other state-of-art algorithms, our proposal improves the prediction F1 score of vehicle mobility by more than 30%, especially for those vehicles that own a strong individual mobility preference.