The present paper accomplished the laminar and chaotic natural convection SPH simulation in a differentially heated square cavity at high Rayleigh number up 10⁹. To our knowledge, there is few reported SPH literature for the natural convection at Ra >10⁶, mainly due to the tensile instability issues with negative pressure and complex vortices at high Rayleigh number. In order to ensure the accuracy and stability at high Rayleigh number, Kernel gradient correction (KGC), particle shifting technology (PST) [1], density correction and two kinds of discrete scheme of pressure gradient [2] are considered. Four different SPH models are assessed for the natural convection at low Rayleigh number 10⁴ and high Rayleigh number 10⁸, respectively. The comparison study shows that delta-sph_minus model is able to ensure the accuracy and stability at high Rayleigh number 10⁸ [3]. Further, the simulation of the natural convection at Ra =10⁹ is conducted using delta-sph_minus model and the evolution of flow structure and heat transfer characteristic are discussed in this study (e.g., Fig. 1).