In this work, Lattice Boltzmann Method (LBM) is used to study the heat transfer by natural convection of a nanofluid (Water-Al2O3) in a square cavity with D2Q9 scheme. This method is used to describe and analyze the flow of nanofluid by convection in a differentially heated cavity. The horizontal walls of the cavity are adiabatic, while the right and left sides are with cold and hot constant temperature, respectively. The macroscopic variables which characterize the flow and the heat transfer by convection (temperature and two components of the velocity) are determined from the mesoscopic variable (distribution functions). The results of this study show the influence of the Rayleigh number and the volume fraction of the nanoparticles on the flow structure and the average Nusselt number. Two correlations of the maximum vertical velocity and the average Nusselt number with Rayleigh number and volume fraction are envisaged.