Geometry images with normal data are a regular representation for approximating realistic 3D meshes, which can be compressed by image codec algorithms. However normal data include too much detailed information, which makes traditional normal images difficult to be compressed efficiently. In this paper, we first propose angle-normal images to reduce the number of normal component channels from three to two and present a predicted-based codec scheme for realistic 3D meshes. The angle-normal images with two angle components of normals are generated by parametrization process corresponding to geometry images. While obtaining compact representation of normal data, some high frequency components exist in the angle-normal images, which can bring high complexity of compression. Therefore, in the proposed codec algorithm, we first propose to predict the angle-normal images by the reconstructed geometry images. Then we introduce the side information for reducing the high frequency components, which can be estimated in the decoder side. Experimental results show that the proposed scheme outperforms the existing compression schemes in terms of both objective and subjective qualities.