Hyperspectral imaging could collect spectrum information of ground objects on the earth surface using hundreds of bands and are widely used in recognizing subtle differences among difference ground objects. Unfortunately, numerous bands with strong intra-band correlations cause unbearable computational burdens in hyperspectral processing, and especially that seriously hinders the classification of Hyperspectral imagery (HSI) in many realistic applications. Therefore, a sparse self-representation (SSR) method was proposed to select proper bands and make dimensionality reduction on HSI data to benefit its further classification procedure. The SSR improves the sparse representation model of multiple measurement vectors (MMV) using the idea that the dictionary matrix is equal to the measurement matrix, and it regards the aimed band subset as the representative from all bands of the HSI dataset. The method formulates the band selection into finding nonzero row vectors of sparse coefficient matrix in MMV, and adopts the mixed norm to constrain the number of nonzero row vectors. The sparse coefficient matrix is solved by using fast alternating direction method of multipliers and nonzero row vectors are clustered to make proper selection from all bands. Two open HSI datasets including Urban and Pavia University are implemented to testify our SSR method and the results are compared with the other four alternative band selection methods. Experimental results show that the SSR achieves comparable even better overall classification accuracies than the linear constrained minimum variance-based band correlation constraint (LCMV-BCC) algorithm and the sparse nonnegative matrix factorization (SNMF) algorithm, whereas the computational speed of SSR significantly outperforms that of LCMV-BCC. The proposed SSR could accordingly be a good alternative to help choose proper bands from hyperspectral images.