Hyperspectral image classification (HSI) has been widely used in many fields. However, image noise, atmospheric conditions, material distribution and other factors seriously degrade the classification accuracy of HSIs. To alleviate these issues, a new approach, namely adaptive weighted quaternion Zernike moments (AWQZM), is proposed, which extracts effective spatial-spectral features for pixels in HSI classification. The main contributions and novelties of the method are as follows: 1) the AWQZM can adaptively set weights for each pixel in the neighborhood, which not only can flexibly search for homogeneous regions of HSIs, but also can strengthen the similarity of pixels from the same class and the distinctiveness of pixels from different classes; 2) the AWQZM can be constructed in a small subset of bands through a grouping strategy, thereby reducing the computational complexity; and 3) the introduction of quaternions can preserve the spatial correlation among bands and reduce the loss of data information, and the use of quaternion phase information makes the extracted features more informative and discriminative. Moreover, the spectral features and spatial features are combined to achieve better HSI classification results. Experimental results on three benchmark data sets demonstrate that the proposed approach achieves better classification performance than other related approaches.