In this paper, we propose a new fragile watermarking scheme for 3D meshes. Firstly, the watermark information is adaptively embedded into the mesh geometry by slightly adjusting the vertex positions while the mesh topology is unchanged. The embedded watermark can be blindly retrieved with some priori knowledge and used to authenticate the integrity of the watermarked mesh. Compared with previous methods, our proposed one has the following advantages: (1) the embedded watermark is invariant to translation, rotation and uniformly scaling, but sensitive to other operations; (2) enhanced with a reference position, any processing made to the watermarked mesh can be detected; (3) the embedding strength is adjustable so that a trivial tampering with the watermarked mesh model may lead the embedded watermark to change. As a result, unauthorized modifications of the mesh model can be detected and classified.