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Band selection is an important preprocessing technique for hyperspectral images to select a band subset with representative information and low correlation. However, most methods focus on removing redundant components without loss of original information, but not distinguishing the noisy and low-discriminating bands which must be manually removed in advance. To find high-discriminating and high-quality bands from the original hyperspectral cube, we propose an importance-assisted column subset band selection (iCSBS) method. First, an active gradient-reference (AGR) index based on iterative reference gradient map is designed to evaluate the importance of each band. Then, the AGR index is incorporated into a column subset selection method to select high-discriminating bands, via simultaneously minimizing the redundancy and maximizing the quality of the selected band subset. Furthermore, as the high dimensionality decreases the contrast between bands, we use Manhattan distance instead of Euclidean distance. The experimental results on three real-world hyperspectral images demonstrate that the proposed method can achieve higher classification accuracy than other state-of-the-art comparison methods, and is especially superior to the geometry-based methods.