Based on the lattice Boltzmann method, the multiple-relaxation-time (MRT) model was selected to simulate the three-dimensional natural convection heat transfer in a cubic cavity with local hot and cold walls. The D3Q19 model and the D3Q7 model were used to describe the velocity field and temperature field, respectively. The effects of different Rayleigh numbers Ra (10³≤Ra≤10⁵) and local hot and cold wall position on the natural convection in the three-dimensional cubic cavity were studied. The results reveal that the arrangement of the hot and cold walls has a significant effect on the flow heat transfer, and the larger the Ra, the more obvious the effect. The strongest natural convection heat transfer capacity is obtained by Case 5 with the hot and cold walls in the middle position. As the Ra increases gradually, the natural convection ability increases and the streamline becomes more complicated. Under the same working case, with the increase of Ra, the average Nusselt number Nu_av also increases gradually, and the heat transfer capacity is stronger. The Nu_av value of Case 5 is the largest at the same Ra, indicating that its natural convection heat transfer capability is the strongest.