In this paper, we propose two algorithms of the Nonnegative Tucker decomposition that contain manifold regularization terms used for capturing the underlying geometric structures, which are applied in clustering of image databases. In general, based on Tucker model in the form of least square estimation, that is to find interpretable basis factors, and achieve the compressed of original data. It usually supposes the structures of the processing databases are global linearity. However, in practical applications, such as the processing arguments of image, video sequence and Electroencephalography data, they are usually within richness structures of nonlinear. Therefore, it is necessary to uncover the underlying structures for achieving an effective application. Hence, in this article, we incorporate Laplacian Eigenmaps i.e., LE and Locally Linear Embedding i.e., LLE as the manifold regularization terms into the least square form of Tucker model. In addition, for the physical meaning of reasonable interpretation consistent with original data, thus, the basis factors and core tensor are constrained to be nonnegative. Finally, the numerical results have demonstrated both two our proposed algorithms can achieve an effective performance among state-of-the-art methods.