Deep learning is a popular method for monaural source separation, and especially for extracting a singing voice from a single-channel song. However, deep learning-based source separation ignores the geometrical structure of the input data. This work develops a novel approach to source separation that is based on non-negative matrix factorization (NMF) and deep recurrent neural networks (DRNN) with a locality-preserving constraint. First, NMF was used to learn patterns from training data. The learned patterns are linearly combined with the output of DRNN. Second, a locality-preserving constraint is developed to exploit the inner-structure of the input data in the DRNN learning process. Experimental results obtained using the MIR-1K dataset reveal that the proposed algorithm outperforms the baselines.