The　fundamental　thermodynamic　functions　of　nanograin　boundaries　in　nanocrystalline　metal　were　derived.　The　Gibbs　free　energy　as　a　function　of　the　excess　volume　and　the　temperature　of　the　nanograin　boundary　was　simulated　and　calculated.　Using　nanocrystalline　Cu　as　an　example,　the　thermodynamic　stability　and　the　nanograin　growth　behavior　of　nanocrystalline　microstructure　were　predicted　by　the　nanocrystalline　thermodynamic　model.　The　thermodynamic　functions　of　nanograin　boundaries　were　introduced　into　the　Cellular　Automation　algorithm,　and　the　temperature-varying　nanograin　growth　process　of　nanocrystalline　Cu　was　simulated.　The　kinetics　features　of　the　nanograin　growth　of　the　nanocrystalline　Cu　confirm　the　predictions　from　the　thermodynamic　model.