Remote sensing image scene classification is one of the most challenging problems in understanding high-resolution remote sensing images. Deep learning techniques, especially the convolutional neural network (CNN), have improved the performance of remote sensing image scene classification due to the powerful perspective of feature learning and reasoning. However, several fully connected layers are always added to the end of CNN models, which is not efficient in capturing the hierarchical structure of the entities in the images and does not fully consider the spatial information that is important to classification. Fortunately, capsule network (CapsNet), which is a novel network architecture that uses a group of neurons as a capsule or vector to replace the neuron in the traditional neural network and can encode the properties and spatial information of features in an image to achieve equivariance, has become an active area in the classification field in the past two years. Motivated by this idea, this paper proposes an effective remote sensing image scene classification architecture named CNN-CapsNet to make full use of the merits of these two models: CNN and CapsNet. First, a CNN without fully connected layers is used as an initial feature maps extractor. In detail, a pretrained deep CNN model that was fully trained on the ImageNet dataset is selected as a feature extractor in this paper. Then, the initial feature maps are fed into a newly designed CapsNet to obtain the final classification result. The proposed architecture is extensively evaluated on three public challenging benchmark remote sensing image datasets: the UC Merced Land-Use dataset with 21 scene categories, AID dataset with 30 scene categories, and the NWPU-RESISC45 dataset with 45 challenging scene categories. The experimental results demonstrate that the proposed method can lead to a competitive classification performance compared with the state-of-the-art methods.