In recent years, cellular communication systems have continued to develop in the direction of intelligence. The demand for cellular networks is increasing as they meet the public’s pursuit of a better life. Accurate prediction of cellular network traffic can help operators avoid wasting resources and improve management efficiency. Traditional prediction methods can no longer perfectly cope with the highly complex spatiotemporal relationships of the current cellular networks, and prediction methods based on deep learning are constantly growing. In this paper, a spatial-temporal parallel prediction model based on graph convolution combined with long and short-term memory networks (STP-GLN) is proposed to effectively capture spatial-temporal characteristics and to obtain accurate prediction results. STP-GLN is mainly composed of a spatial module and temporal module. Among them, the spatial module designs dynamic graph data based on the principle of spatial distance and spatial correlation. It uses a graph convolutional neural network to learn the spatial characteristics of cellular network graph data. The temporal module uses three time series based on the principle of temporal proximity and temporal periodicity. It uses three long and short-term memory networks to learn the temporal characteristics of three time series of cellular network data. Finally, the results learned from the two modules are fused with different weights to obtain the final prediction results. The mean absolute error (MAE), root mean square error (RMSE), and R-squared (R2) are used as the performance evaluation metrics of the model in this paper. The experimental results show that STP-GLN can more effectively capture the spatiotemporal characteristics of cellular network data; compared with the most advanced model in the comparison model on the real cellular traffic dataset in one cell, the RMSE can be improved about 81.7%, the MAE is improved about 82.7%, and the R2 is improved about 2.2%.