Hyperspectral unmixing is a process aiming at identifying the constituent materials and estimating the corresponding fractions from hyperspectral imagery of a scene. Nonnegative matrix factorization (NMF), an effective linear spectral mixture model, has been applied in hyperspectral unmixing during recent years. As the data of hyperspectral imagery analyzed deeper, prior knowledge of some signatures in the scene could be available. In several scenes such as mining areas, a few surface substances like copper and iron are easy to identify through field investigation. Thus, their spectral signatures can be used as prior knowledge to unmix hyperspectral data. In such a context, we propose an NMF based framework for hyperspectral unmixing using such prior knowledge, referred to as NMFupk. Specifically, our algorithm supposes that some spectral signatures in the scene are known and then utilizes the prior knowledge of the spectral signatures to unmix the hyperspectral data. In a series of experiments, we test NMFupk and NMF without prior knowledge on both synthetic and real data. Results achieved demonstrate the efficacy of the proposed algorithm.