In this paper, a novel scheme of the adaptive sampling of block compressive sensing is proposed for natural images. In view of the contents of images, the edge proportion in a block can be used to represent its sparsity. Furthermore, according to the edge proportion, the adaptive sampling rate can be adaptively allocated for better compressive sensing recovery. Given that there are too many blocks in an image, it may lead to a overhead cost for recording the ratio of measurement of each block. Therefore, K-means method is applied to classify the blocks into clusters and for each cluster a kind of ratio of measurement can be allocated. In addition, we design an iterative termination condition to reduce time-consuming in the iteration of compressive sensing recovery. The experimental results show that compared with the corresponding methods, the proposed scheme can acquire a better reconstructed image at the same sampling rate.