In the design of intelligent driving systems, reliable and accurate trajectory prediction of pedestrians is necessary. With the prediction of pedestrians’ trajectory, the possible collisions can be avoided or warned as early as possible by changing the behaviour of intelligent vehicles. The trajectory prediction problem can be considered as a sequence learning problem, in which one of the recurrent neural network (RNN) models called long short term memory (LSTM) has been regarded as a promising method. The authors present a new method for predicting the pedestrian's trajectory, which is called Social-Grid LSTM based on RNN architecture. The proposed method combines the human–human interaction model called social pooling and the Grid LSTM network model. The performance of the proposed method is demonstrated on two available public datasets, and compared with two baseline methods (LSTM and Social LSTM). The experimental results indicate that the authors’ proposed method outperforms previous prediction approaches.