Hyperspectral unmixing addressing spectral variability remains an important challenge. In this field, unmixing methods do not exploit the possible availability of some spectral information that corresponds to known spectra of some pure materials present in an acquired scene. In this work, a hyperspectral unmixing method, which considers not only the spectral variability phenomenon but also exploits one or more available known pure material spectra, is proposed. Such a combination, initially proposed here, constitutes the originality of the conducted work that distinguishes it from other investigations in the hyperspectral unmixing topic. The proposed method, based on an informed nonnegative matrix factorization technique, employs a partial structured additively-tuned linear mixing model that deals with spectral variability. Experimental results, based on real data, show that the designed informed algorithm, which addresses spectral variability, yields very satisfactory results and outperforms tested literature approaches. Thus, such an unmixing algorithm may be used for automatically detecting and mapping, using hyperspectral data, materials of interest whose spectra are known while dealing with their spectral variability.