Recently, deep learning methods based on the combination of spatial and spectral features have been successfully applied in hyperspectral image (HSI) classification. To improve the utilization of the spatial and spectral information from the HSI, this paper proposes a unified network framework using a three-dimensional convolutional neural network (3-D CNN) and a band grouping-based bidirectional long short-term memory (Bi-LSTM) network for HSI classification. In the framework, extracting spectral features is regarded as a procedure of processing sequence data, and the Bi-LSTM network acts as the spectral feature extractor of the unified network to fully exploit the close relationships between spectral bands. The 3-D CNN has a unique advantage in processing the 3-D data; therefore, it is used as the spatial-spectral feature extractor in this unified network. Finally, in order to optimize the parameters of both feature extractors simultaneously, the Bi-LSTM and 3-D CNN share a loss function to form a unified network. To evaluate the performance of the proposed framework, three datasets were tested for HSI classification. The results demonstrate that the performance of the proposed method is better than the current state-of-the-art HSI classification methods.