Blind hyperspectral unmixing (BHSU) is ill-posedness. It aims to obtain accurate and robust endmember signatures and the corresponding abundances simultaneously. Nonnegative matrix factorization (NMF)-based sparsity-regularized algorithms have been widely employed for the BHSU. However, the existing unmixing approaches are sensitive to the multifarious intrinsic interferences and noises, which are caused because of the utilization of the inappropriate loss function to measure the quality of the hyperspectral data (HD) reconstruction and regularization. In this article, we propose a noise-free graph regularized model (NFGRM) by applying the dual graph regularized robust nonnegative matrix tri-factorization (NMTF), which leads to a novel reliable reconstruction of the HD. In the NFGRM, all the challenging interferences are addressed as noises. Consequently, a more faithful approximation is expected to recover from the highly noisy mixed data set and achieve robust regularization by controlling the heteroscedastic noises and the ill-posedness of the BHSU problem simultaneously. Experimental results on synthetic and several benchmark HD sets demonstrate the effectiveness and robustness of the proposed model and algorithm.