Remote sensing (RS) image scene classification task faces many challenges due to the interference from different characteristics of different geographical elements. To solve this problem, we propose a multi-branch ensemble network to enhance the feature representation ability by fusing features in final output logits and intermediate feature maps. However, simply adding branches will increase the complexity of models and decline the inference efficiency. On this issue, we embed self-distillation (SD) method to transfer knowledge from ensemble network to main-branch in it. Through optimizing with SD, main-branch will have close performance as ensemble network. During inference, we can cut other branches to simplify the whole model. In this paper, we first design compact multi-branch ensemble network, which can be trained in an end-to-end manner. Then, we insert SD method on output logits and feature maps. Compared to previous methods, our proposed architecture (ESD-MBENet) performs strongly on classification accuracy with compact design. Extensive experiments are applied on three benchmark RS datasets AID, NWPU-RESISC45 and UC-Merced with three classic baseline models, VGG16, ResNet50 and DenseNet121. Results prove that our proposed ESD-MBENet can achieve better accuracy than previous state-of-the-art (SOTA) complex models. Moreover, abundant visualization analysis make our method more convincing and interpretable.