The large intra-class difference and inter-class similarity of scene images bring great challenges to the research of remote-sensing scene image classification. In recent years, many remote-sensing scene classification methods based on convolutional neural networks have been proposed. In order to improve the classification performance, many studies increase the width and depth of convolutional neural network to extract richer features, which increases the complexity of the model and reduces the running speed of the model. In order to solve this problem, a lightweight convolutional neural network based on hierarchical-wise convolution fusion (LCNN-HWCF) is proposed for remote-sensing scene image classification. Firstly, in the shallow layer of the neural network (groups 1–3), the proposed lightweight dimension-wise convolution (DWC) is utilized to extract the shallow features of remote-sensing images. Dimension-wise convolution is carried out in the three dimensions of width, depth and channel, and then, the convoluted features of the three dimensions are fused. Compared with traditional convolution, dimension-wise convolution has a lower number of parameters and computations. In the deep layer of the neural network (groups 4–7), the running speed of the network usually decreases due to the increase in the number of filters. Therefore, the hierarchical-wise convolution fusion module is designed to extract the deep features of remote-sensing images. Finally, the global average pooling layer, the fully connected layer and the Softmax function are used for classification. Using global average pooling before the fully connected layer can better preserve the spatial information of features. The proposed method achieves good classification results on UCM, RSSCN7, AID and NWPU datasets. The classification accuracy of the proposed LCNN-HWCF on the AID dataset (training:test = 2:8) and the NWPU dataset (training:test = 1:9), with great classification difficulty, reaches 95.76% and 94.53%, respectively. A series of experimental results show that compared with some state-of-the-art classification methods, the proposed method not only greatly reduces the number of network parameters but also ensures the classification accuracy and achieves a good trade-off between the model classification accuracy and running speed.