The spatiotemporal graph modeling is a basic work to analyze the spatial relationship and time trend of each element in the graph structure system. The traditional spatiotemporal graph modeling method is mainly based on the explicit structure of nodes and the fixed relationship between nodes in the graph for spatial relationship mining, which severely limits the flexibility of the model. Besides, traditional methods cannot capture long-term trends. To overcome these shortcomings, a novel end-to-end neural network model for spatiotemporal graph modeling is proposed, i.e., a graph wavelet convolutional neural network for spatiotemporal graph modeling called GWNN-STGM. A graph wavelet convolutional neural network layer is designed in GWNN-STGM. A self-adaption adjacency matrix is introduced in this network layer for node embedding learning so that the model can be used without prior knowledge of the structure. The hidden structural information is automatically found in the training dataset. In addition, GWNN-STGM includes a stacked dilated causal convolutional network layer so that the receptive field of the model can grow exponentially with the increase in the number of convolutional network layers that can handle long-term sequences. The GWNN-STGM successfully integrated the two modules of graph wavelet convolutional neural network layer and dilated causal convolutional network layer. Experimental results on two public transportation network datasets show that the performance of the proposed GWNN-STGM is better than other latest benchmark models, which shows that the designed graph wavelet convolutional neural network model has a great ability to explore the spatial-temporal structure from the input dataset.