Spectral unmixing is an important technology in hyperspectral image applications. Recently, sparse regression is widely used in hyperspectral unmixing. This paper proposes a double reweighted sparse regression method for hyperspectral unmixing. The proposed method enhances the sparsity of abundance fraction in both spectral and spatial domains through double weights, in which one is used to enhance the sparsity of endmembers in the spectral library, and the other to improve the sparseness of abundance fraction of every material. Experimental results on both synthetic and real hyperspectral data sets demonstrate effectiveness of the proposed method both visually and quantitatively.