Wind speed prediction with spatio?temporal correlation is among the most challenging tasks in wind speed prediction. In this paper, the problem of predicting wind speed for multiple sites simultaneously is investigated by using spatio?temporal correlation. This paper proposes a model for wind speed prediction with spatio?temporal correlation, i.e., the predictive deep convolutional neural network (PDCNN). The model is a unified framework, integrating convolutional neural networks (CNNs) and a multi-layer perceptron (MLP). Firstly, the spatial features are extracted by CNNs located at the bottom of the model. Then, the temporal dependencies among these extracted spatial features are captured by the MLP. In this way, the spatial and temporal correlations are captured by PDCNN intrinsically. Finally, PDCNN generates the predicted wind speed by using the learnt spatio?temporal correlations. In addition, three error indices are defined to evaluate the prediction accuracy of the model on the wind turbine array. Experiment results on real-world data show that PDCNN can capture the spatio?temporal correlation effectively, and it outperforms the conventional machine learning models, including multi-layer perceptron, support vector regressor, decision tree, etc.