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