The prediction of vacant parking spaces (VPSs) can reduce the time drivers spend searching for parking, thus alleviating traffic congestion. However, previous studies have mostly focused on modeling the temporal features of VPSs using historical data, neglecting the complex and extensive spatial characteristics of different parking lots within the transportation network. This is mainly due to the lack of direct physical connections between parking lots, making it challenging to quantify the spatio-temporal features among them. To address this issue, we propose a dynamic spatio-temporal adaptive graph convolutional recursive network (DSTAGCRN) for VPS prediction. Specifically, DSTAGCRN divides VPS data into seasonal and periodic trend components and combines daily and weekly information with node embeddings using the dynamic parameter-learning module (DPLM) to generate dynamic graphs. Then, by integrating gated recurrent units (GRUs) with the parameter-learning graph convolutional recursive module (PLGCRM) of DPLM, we infer the spatio-temporal dependencies for each time step. Furthermore, we introduce a multihead attention mechanism to effectively capture and fuse the spatio-temporal dependencies and dynamic changes in the VPS data, thereby enhancing the prediction performance. Finally, we evaluate the proposed DSTAGCRN on three real parking datasets. Extensive experiments and analyses demonstrate that the DSTAGCRN model proposed in this study not only improves the prediction accuracy but can also better extract the dynamic spatio-temporal characteristics of available parking space data in multiple parking lots.