We propose a novel extension of Nonnegative Matrix Factorization (NMF) that models a signal with multiple local dictionaries activated sparsely. This set of local dictionaries for a source, e.g., speech, disjointly constitute a superset that is more discriminative than an ordinary NMF dictionary, because its local structures represent the source's manifold better. A block sparsity constraint is used to regularize the NMF solutions so that only one or a small number of blocks are active at a given time. Moreover, a concentrationz prior further regularizes each block of bases to be close to each other for better locality preservation. We test the proposed Mixture of Local Dictionaries (MLD) on single-channel speech enhancement tasks and show that it outperforms the state of the art technology by up to 2 dB in signal-to-distortion ratio, especially in the unsupervised environment where neither the speaker identity nor the type of noise is known in advance.