Connected and Automated Vehicles (CAV) have been rapidly developed, which, inevitably, renders that human-driven and autonomous vehicles share the road. Thus, trajectory prediction is an important research topic, which helps each CAV to efficiently follow a Human-Driven Vehicle (HV). In a wider scope, trajectory prediction, also, helps to improve the throughput of traffic flow and enhance its stability. To realize the trajectory prediction of Connected and Automated Vehicles to Human-Driven Vehicles, a car-following model, which is based on trajectory data, was established. Adding deep neural networks and an Attention mechanism, this paper established a data-driven car-following model, based on CNN-BiLSTM-Attention for CAV, to predict trajectory, by referring to the modeling idea of the traditional car-following model. The trajectory data in the next-generation-simulation (NGSIM) datasets that match the car-following characteristics were selected. In addition, noise-reduction pre-processing of the trajectory data was performed, to make it match the actual car-following situation. Experiments, for selecting the optimal structure of the model and the method of trajectory prediction, were carried out. The data-driven car-following models, such as LSTM, GRU, and CNN-BiLSTM, were selected for comparative analysis of trajectory prediction. The results show that the CNN-BiLSTM-Attention model has the smallest MAE and MSE as well as the largest R2. The CNN-BiLSTM-Attention model has the highest accuracy in vehicle-trajectory prediction. The model can, effectively, realize vehicle-trajectory prediction and provide a theoretical basis for vehicle-trajectory-based velocity guidance of Human-Driven Vehicles. In the future, the model can, also, provide the theoretical basis for Connected and Automated Vehicles, to make car-following decisions in mixed traffic flow.