Nonnegative Tucker Decomposition (NTD) is one of the most popular technique for feature extraction and representation from nonnegative tensor data with preserving internal structure information. From the perspective of geometry, highdimensional data are usually drawn in low-dimensional submanifold of the ambient space. In this paper, we propose a novel Graph reguralized Nonnegative Tucker Decomposition (GNTD) method which is able to extract the low-dimensional parts-based representation and preserve the geometrical information simultaneously from high-dimensional tensor data. We also present an effictive algorithm to solve the proposed GNTD model. Experimental results demonstrate the effectiveness and high efficiency of the proposed GNTD method.