Scene classification of remote sensing (RS) images has attracted increasing attention due to its wide applications. Recently, with the advances of deep learning models, especially convolutional neural networks (CNNs), the performance of remote sensing image scene classification has been significantly improved. In this paper, based on the popular CNN, we develop a new scene classification network, named the Global and Local Consistent (GLC) network, to deeply explore useful information from the RS images. First, we adopt a pre-trained CNN to learn the intermediate feature maps from the RS image pairs. Second, by introducing the visual attention mechanism, the global and local integration model is developed to mine the rich information from the obtained feature maps. Third, the attention consistent model is designed to eliminate the negative influence of the issue of attention inconsistency on the classification. To verify the effectiveness of the proposed method, we select two popular RS image data sets. Compared with some existing classification models, our network can achieve competitive results, which illustrates that our method is useul to the RS scene classification.