Generative　adversarial　network　(GAN)　has　become　a　hot　research　in　artificial　intelligence,　and　has　received　much　attention　from　scholars.　In　view　of　low　efficiency　of　generative　model　and　gradient　disappearance　of　discriminative　model,　a　GAN　based　on　energy　function　(E-REGAN)　is　proposed　in　this　paper,　in　which　reconstruction　error　(RE)　acts　as　the　energy　function.　Firstly,　an　adaptive　deep　belief　network　(ADBN)　is　presented　as　the　generative　model,　which　is　used　to　fast　learn　the　probability　distribution　of　given　sample　data　and　further　generate　new　data　with　similar　probability　distribution.　Secondly,　the　RE　in　adaptive　deep　auto-encoder　(ADAE)　acts　as　an　energy　function　evaluating　the　performance　of　discriminative　model;　the　smaller　energy　function,　the　closer　to　Nash　equilibrium　the　learning　optimization　process　of　GAN　will　be,　and　vice　versa.　Meanwhile,　the　stability　analysis　of　the　proposed　E-REGAN　is　given　using　the　inverse　inference　method.　Finally,　the　simulation　results　from　MNIST　and　CIFAR-10　benchmark　dataset　experiments　show　that,　compared　with　the　existing　similar　models,　the　proposed　E-REGAN　achieves　significant　improvement　in　learning　rate　and　data　generation　capability.　Copyright　©　2018　Acta　Automatica　Sinica.　All　rights　reserved.