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Thermal convection is a fundamental phenomenon found in many atmospheric and industrial applications.Many numerical methods have been applied to analyze this problem,including the lattice Boltzmann method (LBM), which has emerged as one of the most powerful computational fluid dynamics (CFD) methods in recent years.Using a simple LB model with the Boussinesq approximation, this study investigates the 2D RayleighBe nard problem from the threshold of the primary instability with a theoretical value of critical Rayleigh number Rac=1707.76 to the regime near the flow bifurcation to the secondary instability.A simple LB model is used to simulate natural convection, 2D turbulence Rayleigh-Be nard convection and 3D turbulence Rayleigh-Be nard convection.Finally, the relationship between the Nusselt number and the Rayleigh number is also investigated.