As an effective heat transfer medium, Nanofluid is used widely in heat transfer field. However, due to the contradiction between the heat conductivity coefficient of nanofluid and the cost of nanoparticles, a new mixed nanofluid is developed. In order to investigate the natural convection heat transfer characteristics and the interaction mechanism between nanoparticles, the lattice Boltzmann equations of nanofluid flow and temperature fields are deduced by multi-scale technique based on considering the interaction forces between nanoparticles, and the lattice Boltzmann model of Cu/Al2O3-water mixed nanofluid is established by coupling the evolution equations of flow with temperature fields. Nanoparticles distribution in enclosure and interaction forces between nanoparticles are investigated, it is found that Brownian motion force is far bigger than any other forces, and the effects of temperature difference driving force and Brownian motion force on nanoparticles distribution are biggest. In addition, the effects of nanoparticles fractions and Rayleigh number on natural convection are investigated, and the natural convection heat transfer characteristics of mixed nanofluid (Cu/Al2O3-water) are compared with those of single metal nanoparticle nanofluid (Al2O3-water). It is found that the mixed nanofluid has a higher heat transfer characteristic than other common nanofluid.