Image authentication is a technique aiming at protecting the integrity of digital images. Reversible image authentication has attracted much attention of researcher because it allows to authenticate tampered regions in the image and to reconstruct the stego image to its original version losslessly. In this paper, we propose a new, reversible image authentication scheme based on adaptive prediction error expansion (PEE) technique. In the proposed scheme, each image block is classified into smooth or complex regions. Then, according to the characteristic of each block, the authentication code is embedded adaptively to achieve high performance of tamper detection. The experimental results demonstrated that the proposed scheme achieves good quality of stego images. In addition, the proposed scheme has ability to reconstruct the stego image to its original version, if no modification is performed on it. Also demonstrated in the experimental results, the proposed scheme provides higher accuracy of tamper detection than state-of-the-art schemes.