Vehicle position prediction (VPP) is of great significance for navigation planning and traffic safety of intelligent vehicles. In general, particle filtering (PF) uses global navigation satellite system (GNSS) to implement VPP. However, it does not consider geographic layer information (GLI) and its particle weight is not combined with the real-world geographic position information, which leads to insufficient prediction preparation. To resolve this problem, we propose a novel PF-based VPP method by using three-dimensional convolutional neural network and long short-term memory (3D CNN-LSTM) network model. First, for data preprocessing, we extract kinematic information features from GNSS, and evenly divide the area around each GNSS point into multiple grids and calculate the probability of grids center belonging to each GLI type. In addition, in order to better reflect the relationship between two consecutive positions due to the factors such as the conversion angle, we construct tilted cells to represent possible positions of each vehicle at any time. Second, a novel 3D CNN-LSTM model is designed to calculate the vehicle occurrence probability (VOP) in each tilted cell by processing the GLI and GNSS data, which can optimize the PF weight of each particle, and then improve PF to make more precise position prediction. Finally, the experimental results demonstrate that the proposed VPP method can improve the cell prediction accuracy, and then significantly improve the position prediction precision.