Trajectory prediction is a fundamental and challenging task for numerous applications, such as autonomous driving and intelligent robots. Current works typically treat pedestrian trajectories as a series of 2D point coordinates. However, in real scenarios, the trajectory often exhibits randomness, and has its own probability distribution. Inspired by this observation and other movement characteristics of pedestrians, we propose a simple and intuitive movement description called a trajectory distribution, which maps the coordinates of the pedestrian trajectory to a 2D Gaussian distribution in space. Based on this novel description, we develop a new trajectory prediction method, which we call the social probability method. The method combines trajectory distributions and powerful convolutional recurrent neural networks. Both the input and output of our method are trajectory distributions, which provide the recurrent neural network with sufficient spatial and random information about moving pedestrians. Furthermore, the social probability method extracts spatio-temporal features directly from the new movement description to generate robust and accurate predictions. Experiments on public benchmark datasets show the effectiveness of the proposed method.