In this paper, we propose a spectral-spatial unified network (SSUN) with an end-to-end architecture for the hyperspectral image (HSI) classification. Different from traditional spectral-spatial classification frameworks where the spectral feature extraction (FE), spatial FE, and classifier training are separated, these processes are integrated into a unified network in our model. In this way, both FE and classifier training will share a uniform objective function and all the parameters in the network can be optimized at the same time. In the implementation of the SSUN, we propose a band grouping-based long short-term memory model and a multiscale convolutional neural network as the spectral and spatial feature extractors, respectively. In the experiments, three benchmark HSIs are utilized to evaluate the performance of the proposed method. The experimental results demonstrate that the SSUN can yield a competitive performance compared with existing methods.