In this paper, a novel fragile watermarking is proposed. It is different from the common fragile watermarking, which uses the cryptographic digital signature of an image or image blocks as authentication information, because two new conceptions, mass and centroid in physics are introduced into our scheme and the fragile watermarking is designed based on them. The mass and the position of centroid are used as authentication information for the image block. Since two random sequences are applied to randomize the abscissa and ordinate of an image block’s centroid, the algorithm can successfully avoid the drawback of cryptographic hash function, which suffers the famous birthday attack. When attackers tamper the image, the mass and the position of centroid are changed, with the changes of them, we can effectively locate the tamper done to the image. Experimental results show that this watermarking can detect and locate any change made to an image.