Unlike　images,　the　topology　similarity　among　meshes　can　hardly　be　handled　with　traditional　signal　processing　tools　because　of　their　irregular　structures.　Geometry　image　parameterization　provides　a　way　to　represent　3D　meshes　in　the　form　of　2D　geometry　and　normal　images.　However,　most　existing　methods,　including　the　CoGAN　are　not　suitable　for　such　unnatural　images　corresponding　to　meshes.　To　solve　this　problem,　we　propose　a　Prediction　Generative　Adversarial　Network　(PGAN)　to　learn　a　joint　distribution　of　geometry　and　normal　images　for　generating　meshes.　Particularly,　we　enforce　a　prediction　constraint　on　the　geometry　GAN　and　normal　GAN　in　our　PGAN　utilizing　the　inherent　relationship　between　the　geometry　and　normal.　The　experimental　results　on　face　mesh　generation　indicate　that　our　PGAN　outperforms　in　generating　realistic　face　models　with　rich　facial　attributes　such　as　facial　expression　and　retaining　the　geometry　of　the　faces.　©　2019　IEEE.