The purpose of single source separation is to recover a particular signal from a mixed signal. This work develops a novel source separation method for use with an automatic speech recognition (ASR) system. The proposed method is based on non-negative matrix factorization (NMF), which is extensively used in single channel source separation. In the cost function, a flexible distance, αβ-divergence, is used. Additionally, a mixture signal in high-dimensional space contains a low-dimensional manifold. To preserve this embedded structure, a graph regularization constraint is added to the objective function for optimization. The experimental results thus obtained reveal that the proposed method outperforms baseline methods.