Intersections are quite important and complex traffic scenarios, where the future motion of surrounding vehicles is an indispensable reference factor for the decision-making or path planning of autonomous vehicles. Considering that the motion trajectory of a vehicle at an intersection partly obeys the statistical law of historical data once its driving intention is determined, this paper proposes a long short-term memory based (LSTM-based) framework that combines intention prediction and trajectory prediction together. First, we build an intersection prior trajectories model (IPTM) by clustering and statistically analyzing a large number of prior traffic flow trajectories. The prior trajectories model with fitted probabilistic density is used to approximate the distribution of the predicted trajectory, and also serves as a reference for credibility evaluation. Second, we conduct the intention prediction through another LSTM model and regard it as a crucial cue for a trajectory forecast at the early stage. Furthermore, the predicted intention is also a key that is associated with the prior trajectories model. The proposed framework is validated on two publically released datasets, next generation simulation (NGSIM) and INTERACTION. Compared with other prediction methods, our framework is able to sample a trajectory from the estimated distribution, with its accuracy improved by about 20%. Finally, the credibility evaluation, which is based on the prior trajectories model, makes the framework more practical in the real-world applications.