Autonomous vehicles (AVs) need to adequately predict the trajectory space of surrounding vehicles (SVs) in order to make reasonable decision-making and improve driving safety. In this paper, we build the driving behavior intention recognition module and traffic vehicle expected trajectory prediction module by deep learning. On the one hand, the driving behavior intention recognition module identifies the probabilities of lane keeping, left lane changing, right lane changing, left acceleration lane changing, and right acceleration lane changing of the predicted vehicle. On the other hand, the expected trajectory prediction module adopts an encoder-decoder architecture, in which the encoder encodes the historical environment information of the surrounding agents as a context vector, and the decoder and MDN network combine the context vector and the identified driving behavior intention to predict the probability distribution of future trajectories. Additionally, our model produces the multiple behaviors and trajectories that may occur in the next 6 s for the predicted vehicle (PV). The proposed model is trained, validated and tested with the HighD dataset. The experimental results show that the constructed probabilistic multi-modal expected trajectory prediction possesses high accuracy in the intention recognition module with full consideration of interactive information. At the same time, the multi-modal probability distribution generated by the anticipated trajectory prediction model is more consistent with the real trajectories, which significantly improves the trajectory prediction accuracy compared with other approaches and has apparent advantages in predicting long-term domain trajectories.