Traditional 2D face recognition has been studied for many years and has achieved great success. Nonetheless, there is high demand to explore unrevealed information other than structure and texture in spatial domain in the faces. Hyperspectral imaging meets such requirements by providing additional spectrum information on objects, in completion to the traditional spatial features extracted in 2D images. In this paper, we propose a novel 3D high-order texture pattern descriptor for hyperspectral face recognition, which effectively exploit both spatial and spectral features in hyperspectral images. Based on the local derivative pattern, our method encodes the hyperspectral faces with multi-directional derivatives and binarization function in spatial-spectral space. Then a spatial-spectral feature descriptor is generated by applying a 3D histogram on the derivative pattern, which can be used to convert hyperspectral face images into vectorized representations. Compared to traditional face recognition methods, our method is able to describe the distinctive micro-patterns which integrate the spatial and spectral information in faces. Experiments on the real hyperspectral face datasets prove that our method has outperformed several state-of-the-art hyperspectral face recognition approaches.