In the framework of block compressed sensing (BCS), the reconstruction algorithm based on the smoothed-projected Landweber iteration can achieve better performance of rate-distortion with a low computational complexity, especially for the case using the principle component analysis (PCA) to conduct adaptive hard-thresholding shrinkage. However, during learning PCA matrix, the reconstruction performance of Landweber iteration is affected because of neglecting the stationary local structural characteristic of image. To solve the above problems, the granular computing (GrC) is adopted to decompose an image into several granules depending on the structural features of patches, and then PCA is performed to learn the sparse representation basis corresponding to each granule. Finally, the hard-thresholding shrinkage is used to remove the noises in patches. The patches in granule have the stationary local structural characteristic, and the proposed method can thus effectively improve the performance of hard-thresholding shrinkage. Experimental results indicate that the reconstructed image by the proposed algorithm has a better objective quality when comparing with several traditional ones, and its edge and texture details are better preserved, which guarantees the better subjective visual quality. Besides, the method has a low computational complexity of reconstruction.