Short-term traffic flow prediction is a core branch of intelligent traffic systems (ITS) and plays an important role in traffic management. The graph convolution network (GCN) is widely used in traffic prediction models to efficiently handle the graphical structural data of road networks. However, the influence weights among different road sections are usually distinct in real life and are difficult to analyze manually. The traditional GCN mechanism, which relies on a manually set adjacency matrix, is unable to dynamically learn such spatial patterns during training. To address this drawback, this study proposes a novel location graph convolutional network (location-GCN). The location-GCN solves this problem by adding a new learnable matrix to the GCN mechanism, using the absolute value of this matrix to represent the distinct influence levels among different nodes. Subsequently, long short-term memory (LSTM) is employed in the proposed traffic prediction model. Moreover, trigonometric function encoding was used in this study to enable the short-term input sequence to convey long-term periodic information. Finally, the proposed model was compared with the baseline models and evaluated on two real-world traffic flow datasets. The results show that our model is more accurate and robust than the other representative traffic prediction models.