Given a spectral library, sparse unmixing aims at finding the optimal subset of endmembers from it to model each pixel in the hyperspectral scene. However, sparse unmixing still remains a challenging task due to the usually high mutual coherence of the spectral library. In this paper, we exploit the spectral a priori information in the hyperspectral image to alleviate this difficulty. It assumes that some materials in the spectral library are known to exist in the scene. Such information can be obtained via field investigation or hyperspectral data analysis. Then, we propose a novel model to incorporate the spectral a priori information into sparse unmixing. Based on the alternating direction method of multipliers, we present a new algorithm, which is termed sparse unmixing using spectral a priori information (SUnSPI), to solve the model. Experimental results on both synthetic and real data demonstrate that the spectral a priori information is beneficial to sparse unmixing and that SUnSPI can exploit this information effectively to improve the abundance estimation.