Intelligent parking guidance systems (IPGSs) based on vacant parking space (VPS) availability predictions are highly effective to alleviate the increasingly serious parking difficulties in metropolis. The spatial-temporal correlation analysis of VPS information of multiple parking lots in a region shows that not only the number of VPS in each parking lot has a stable temporal correlation, but also there is obvious spatial correlation among different parking lots. Given this, this paper takes full advantage of the space-time correlation and makes short-term (within 30 min) and long-term (over 30 min) predictions about the number of VPSs in multiple parking lots in an area parallelly. Specifically, this paper develops a deep gated graph recurrent neural network (G <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> RNN) model which has the ability to extract both spatial and temporal correlations concurrently between different parking lots. The advantages of the G <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> RNN model are that, first, spatial and temporal correlations between different parking lots can be accurately obtained simultaneously, and second, there is no need to grid the raw data since it uses graph-structured data. For long-term predictions, two different approaches, namely the single-step and iterative predictions, are investigated. The performance of the G <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> RNN based prediction method is extensively evaluated with practical data collected from eight public parking lots in Santa Monica. The results show that it can achieve considerably high accuracy in both short-term and long-term predictions.