The urban rail transit passenger flow origin-destination (OD) matrix has temporal correlation, spatial correlation. According to the spatio-temporal characteristics of passenger flow OD, a short-term prediction method based on long short-term memory (LSTM) neural network and graph convolution network (GCN) is proposed. The proposed prediction method uses the LSTM neural network to capture the temporal correlation, employs the GCN to capture the spatial correlation of the passenger flow, and builds the passenger flow OD matrix based on exit stations to train and test the passenger flow of the whole road network. The experiment shows that the short-term prediction modelled by combing LSTM neural network and GCN can predict the urban rail transit passenger flow OD more effectively. Compared with the single LSTM neural network, the proposed method reduces the prediction error, and is more suitable for short-term passenger flow OD prediction.