Hyperspectral image classification is a basic operation for understanding and applying hyperspectral images, and its accuracy is a key index for measuring the performance of the algorithm used. A novel two-branch residual network (DSSRN) is proposed that can extract robust features of hyperspectral images and is applicable to hyperspectral image classification for improving classification accuracy. First, the Laplace transform, principal component analysis (PCA), and data-amplification methods are used to preprocess hyperspectral image data, enhance image features, remove redundant information, and increase the number of samples. Subsequently, an attention mechanism and a two-branch residual network are used, where spectral and spatial residual networks are adopted in each branch to extract spectral and spatial information as well as to generate one-dimensional feature vectors. Finally, image-classification results are obtained using the fully connected layer. Experiments are conducted on remote-sensing datasets at the Indian Pine, University of Pavia, and Kennedy Space Center. Compared with the two-branch ACSS-GCN, the classification accuracy of proposed model shows 1.94、0.27、20.85 percentage points improvements on the three abovementioned datasets, respectively.