A reversible watermarking scheme extracts the embedded watermarks and then recovers the original image from the watermarked image. This study presents a reversible image watermarking scheme based on the proposed block centering difference method and the absolute histogram modulation method. The block centering difference method calculates the differences between pixels from the center to the outside of a 5x5 block. Thus, the absolute values of pixel differences are always restricted in a small range, so as that the number of peak value in the histogram of a 5x5 block is higher than that of the whole image. The modified absolute histogram modulation method embeds watermarks into both positive and negative differences in a 5x5 block. Experimental results indicate that the quality of watermarked image and the embedded capacity are good. Comparisons with other works demonstrate the excellent performance of the proposed scheme.