This paper proposes a novel fragile watermarking scheme for digital image authentication which is based on Singular Value Decomposition(SVD) and grouped blocks. The watermark bits which include two types of bits are inserted into the least significant bit(LSB) plane of the host image using the adaptive chaotic map to determine the positions. The groped blocks break the block-wise independence and therefore can withstand the Vector Quantization attack(VQ attack). The inserting positions are related to the statistical information of image block data, in order to increase the security and provide an auxiliary way to authenticate the image data. The effectiveness of the proposed scheme is checked by a variety of attacks, and the experimental results prove that it has a remarkable tamper detection ability and also has a precise locating ability.