According to the restoration and reconstruction of the grain boundaries in a metallographical image and the important role of mathematical morphology in image processing, the influences of traditional dilation of mathematical morphology on the gray-scale continuity of an image was demonstrated theoretically, and the relationship between the degree of influence and the sizes of structural elements was discussed. Then, an improved definition for the traditional dilation was proposed. A multi-scale geodesic dilation algorithm was presented to restore and reconstruct the grain boundaries based on the improved definition of dilation. First, the metallographical image was preprocessed based on the improved definition of dilation. Second, the seeds of the grains in the metallographical image were gotten by the methods of multi-scale iterative erosion and geodesic dilation. Finally, the grain boundaries in the metallographical image were obtained by the algorithm of conditioned dilation. Experimental results show that the proposed algorithm is not only faster than the traditional methods of geodesic dilation in the restoration and reconstruction of the grain boundary, but also can obtain the grain boundaries with more clearness, accuracy, continuity and smoothness.