Open public places, such as pedestrian streets, parks, and squares, are vulnerable when the pedestrians thronged into the sidewalks. The crowd count changes dynamically over time with various external factors, such as surroundings, weekends, and peak hours, so it is essential to predict the accurate and timely crowd count. To address this issue, this study introduces graph convolutional network (GCN), a network-based model, to predict the crowd flow in a walking street. Compared with other grid-based methods, the model is capable of directly processing road network graphs. Experiments show the GCN model and its extension STGCN consistently and significantly outperform other five baseline models, namely HA, ARIMA, SVM, CNN and LSTM, in terms of RMSE, MAE and R2. Considering the computation efficiency, the standard GCN model was selected to predict the crowd. The results showed that the model obtains superior performances with higher prediction precision on weekends and peak hours, of which R2 are above 0.9, indicating the GCN model can capture the pedestrian features in the road network effectively, especially during the periods with massive crowds. The results will provide practical references for city managers to alleviate road congestion and help pedestrians make smarter planning and save travel time.