Due to significant performance in the representation of data points, non-negative matrix factorization (NMF) has been widely applied in machine-learning fields, such as dimension reduction, image representation, feature extraction, data mining, and so on. However, classical NMF suffers from a common issue, low efficiency in representing the internal geometric structure of data and sparsity limitation. To circumvent this problem, we innovatively propose a semi-supervised NMF algorithm called semi-supervised dual-graph regularization non-negative matrix factorization (LOSDNMF), into which dual-graph and bi-orthogonal constraints are embedded to reduce the inconsistency between the original matrix and the basic vectors while maintaining the manifold structures of the data and feature spaces. This strategy can fully explore the potential geometry information of the data, which is extremely beneficial to enhance the learning ability of the model. In addition, the local coordinate constraints are introduced to ensure good sparsity of the coefficient matrix and simplify the calculation. Furthermore, an iterative updating scheme for the optimization problem of LOSDNMF and its convergence proofs are also provided in detail. The effectiveness of the proposed method is verified on eight benchmark datasets. Experimental results show that our method can effectively improve clustering performance.