Compressed sensing theory breaks through the limit that two times the bandwidth of the signal sampling rate in Nyquist theorem, providing a guideline for new methods for image acquisition and compression. For still images, block compressed sensing (BCS) has been designed to reduce the size of sensing matrix and the complexity of sampling and reconstruction. However, BCS algorithm assigns the same sampling rate for all image blocks without considering the structures of the blocks. In this paper, we present an adaptive sampling rate assignment method for BCS of images using wavelet transform. Wavelet coefficients of an image can reflect the structure information. Therefore, adaptive sampling rates are calculated and assigned to image blocks based on their wavelet coefficients. Several standard test images are employed to evaluate the performance of the proposed algorithm. Experimental results demonstrate that the proposed algorithm provides superior performance on both the reconstructed image quality and the visual effect.