The movement of pedestrians involves temporal continuity, spatial interactivity, and random diversity. As a result, pedestrian trajectory prediction is rather challenging. Most existing trajectory prediction methods tend to focus on just one aspect of these challenges, ignoring the temporal information of the trajectory and making too many assumptions. In this paper, we propose a Recurrent Attention and Interaction (RAI) model to predict pedestrian trajectories. The RAI model consists of a temporal attention module, spatial pooling module, and randomness modeling module. The temporal attention module is  proposed to assign different weights to the input sequence of a target, and reduce the speed deviation of different pedestrians. The spatial pooling module is proposed to model not only the social information of neighbors in historical frames, but also the intention of neighbors in the current time. The randomness modeling module is proposed to model the uncertainty and diversity of trajectories by introducing random noise. We conduct extensive experiments on several public datasets. The results demonstrate that our method outperforms many that are stateof-the-art.