Precise prediction on vacant parking space (VPS) information plays a vital role in intelligent transportation systems for it helps drivers to find the parking space quickly to reduce unnecessary waste of time and excessive environmental pollution. By analyzing the historical zone-wise VPS data, we find that for the number of VPSs, there is not only a solid temporal correlation within each parking lot, but also an obvious spatial correlation among different parking lots. Given this, this paper proposes a hybrid deep learning framework, known as the dConvLSTM-DCN (dual Convolutional Long Short-Term Memory with Dense Convolutional Network), to make short-term (within 30 min) and long-term (over 30 min) predictions on the VPS availability zone-wisely. Specifically, the temporal correlations of different time scales, namely the 5-min and daily-wise temporal correlations of each parking lot, and the spatial correlations among different parking lots can be effectively captured by the two parallel ConvLSTM components, and meanwhile, the dense convolutional network is leveraged to further improve the propagation and reuse of features in the prediction process. Besides, a two-layer linear network is used to extract the meta-info features to promote the prediction accuracy. For long-term predictions, two methods, namely the direct and iterative prediction methods, are developed. The performance of the prediction model is extensively evaluated with practical data collected from nine public parking lots in Santa Monica. The results show that the dConvLSTM-DCN framework can achieve considerably high accuracy in both short-term and long-term predictions.