Hyperspectral imagery provides abundant spectral information beyond the visible RGB bands, offering rich discriminative details about objects in a scene. Leveraging such data has the potential to enhance visual tracking performance. In this paper, we propose a hyperspectral object tracker based on hybrid attention (HHTrack). The core of HHTrack is a hyperspectral hybrid attention (HHA) module that unifies feature extraction and fusion within one component through token interactions. A hyperspectral bands fusion (HBF) module is also introduced to selectively aggregate spatial and spectral signatures from the full hyperspectral input. Extensive experiments demonstrate the state-of-the-art performance of HHTrack on benchmark Near Infrared (NIR), Red Near Infrared (Red-NIR), and Visible (VIS) hyperspectral tracking datasets. Our work provides new insights into harnessing the strengths of transformers and hyperspectral fusion to advance robust object tracking.