Hyperspectral video camera captures spatial, spectral and temporal information of moving objects. Traditional object tracking methods developed for color videos have been applied to hyperspectral videos after compressing hundreds of spectral bands into three, which does not fully utilize the wealth spectral information. In order to address this issue, we present a tensor sparse correlation filter with a spatial-spectral weighted regularizer for object tracking. First, tensor processing is employed to reduce the spectral differences of homogeneous background, thereby producing robust spectral structure features. Second, a spatial-spectral weighted regularizer is designed in the correlation filter framework to penalize filter template by suppressing spectral features dissimilar to the center pixel in tracking. Third, a sparse constraint term and tracking context information are incorporated to suppress unexpected peaks in the response map. Finally, a reformulated stacked HOG feature extractor and a two-dimensional adaptive scale search strategy are developed to further improve the tracker’s feature discrimination and scale adaptation capability. Experimental results demonstrate that the proposed method achieves superior tracking performance than traditional correlation filter-based trackers.