The hyperspectral image (HSI) classification task is widely used in remote sensing image analysis. The HSI classification methods based on convolutional neural networks (CNNs) have greatly improved the classification performance. However, they cannot well utilize the sequential properties of spectral features and face the challenge of increasing computational cost with the increase in network depth. To address these shortcomings, this paper proposes a novel network with a CNN-Mamba architecture, called DBMamba, which uses a bidirectional Mamba to process spectral feature sequences at a linear computational cost. In the DBMamba, principal component analysis (PCA) is first used to extract the main features of the data. Then, a dual-branch CNN structure, with the fused features from spectral–spatial features by 3D-CNN and spatial features by 2D-CNN, is used to extract shallow spectral–spatial features. Finally, a bidirectional Mamba is used to effectively capture global contextual information in features and significantly enhance the extraction of spectral features. Experimental results on the Indian Pines, Salinas, and Pavia University datasets demonstrate that the classification performance surpasses that of many cutting-edge methods, improving by 1.04%, 0.15%, and 0.09%, respectively, over the competing SSFTT method. The research in this paper enhances the existing knowledge on HSI classification and provides valuable insights for future research in this field.