In this paper, we propose an alternating directional 3D quasi-recurrent neural network for hyperspectral image (HSI) denoising, which can effectively embed the domain knowledge — structural spatio-spectral correlation and global correlation along spectrum. Specifically, 3D convolution is utilized to extract structural spatio-spectral correlation in an HSI, while a quasi-recurrent pooling function is employed to capture the global correlation along spectrum. Moreover, alternating directional structure is introduced to eliminate the causal dependency with no additional computation cost. The proposed model is capable of modeling spatio-spectral dependency while preserving the flexibility towards HSIs with arbitrary number of bands. Extensive experiments on HSI denoising demonstrate significant improvement over state-of-the-arts under various noise settings, in terms of both restoration accuracy and computation time. Our code is available at https://github.com/Vandermode/QRNN3D.