Based on the Grey prediction theory, we propose in this paper a two-pass algorithm for the sharpening of images. In the first pass, pixels around edges or boundaries are detected with edge detection mechanism. During the second pass, those pixels detected as around edges or boundaries are adjusted for the purpose of image sharpening, and those non-edge pixels are kept unaltered. With the proposed approach, most of the original information contained in the image can be retained. In the second pass, the magnitude, i.e., the increment or decrement, to be added to those edge pixels has to be determined. Usually, a larger additive can have a better sharpening result. However it can also lead to the saturation of intensity around edge pixels. Aimed to find the maximal additive magnitude automatically, we proposed in this paper the use of a Grey prediction model GM(1,1) so that the condition of over-sharpening in images to be sharpened can be avoided. In addition, a scaling factor can also be used for the adjustment of the additive magnitude in the proposed approach. Extensive experiments on natural images as well as medical images are also given in this paper. As we will see in the experiments, the proposed approach can have a very distinct intensity transition for pixels around edges or boundaries in the sharpened images, which demonstrates the usefulness of the proposed approach.