Unlike　natural　images,　the　topology　similarity　among　meshes　can　hardly　be　handled　with　classical　deep　learning　because　of　their　irregular　structures.　Parameterization　provides　a　way　to　represent　meshes　in　the　form　of　geometry　and　normal　images,　which　reflects　the　correlation　between　neighboring　sample　locations.　Generative　Adversarial　Networks　(GANs)　can　efficiently　generate　images　without　explicitly　computing　probability　densities　of　the　underlying　distribution.　However,　existing　GANs　such　as　Coupled　Generative　Adversarial　Network　(CoGAN)　generally　have　two　drawbacks:　(1)　Inability　to　process　unnatural　images.　(2)　Insufficient　exploration　of　the　inherent　relation　between　normal　and　the　corresponding　geometry　image.　To　address　these　issues,　this　paper　proposes　an　efficient　method　named　Prediction-Compensation　Generative　Adversarial　Network　(PCGAN)　to　learn　a　joint　distribution　of　both　geometry　and　normal　images,　which　aims　for　generating　meshes　with　two　GANs.　The　consistency　of　two　GANs　for　the　geometry　and　the　normal　is　guaranteed　by　utilizing　a　sequence　of　prediction-compensation　pairs.　The　sequence　can　estimate　the　normal　image　from　the　geometry　image　and　compensate　the　geometry　from　normal　progressively.　Particularly,　the　prediction　has　a　closed-form　expression,　which　provides　high　estimation　accuracy　and　reduces　training　complexity.　Extensive　experimental　results　on　facial　mesh　generation　indicate　that　our　PCGAN　outperforms　CoGAN　and　other　architectures　in　retaining　the　geometry　of　the　faces　and　in　generating　realistic　face　meshes　with　rich　facial　attributes　such　as　facial　expression　and　morphology.　Moreover,　quantitative　evaluations　demonstrate　our　superior　performance　compared　with　the　methods　mentioned　above.