As a vital component in autonomous driving, accurate trajectory prediction effectively prevents traffic accidents and improves driving efficiency. To capture complex spatial-temporal dynamics and social interactions, recent studies developed models based on advanced deep-learning methods. On the other hand, recent studies have explored the use of deep generative models to further account for trajectory uncertainties. However, the current approaches demonstrating indeterminacy involve inefficient and time-consuming practices such as sampling from trained models. To fill this gap, we proposed a novel model named Graph Recurrent Attentive Neural Process (GRANP) for vehicle trajectory prediction while efficiently quantifying prediction uncertainty. In particular, GRANP contains an encoder with deterministic and latent paths, and a decoder for prediction. The encoder, including stacked Graph Attention Networks, LSTM and 1D convolutional layers, is employed to extract spatial-temporal relationships. The decoder is used to learn a latent distribution and thus quantify prediction uncertainty. To reveal the effectiveness of our model, we evaluate the performance of GRANP on the highD dataset. Extensive experiments show that GRANP achieves state-of-the-art results and can efficiently quantify uncertainties. Additionally, we undertake an intuitive case study that showcases the interpretability of the proposed approach. The code is available at https://github.com/joy-driven/GRANP.