Heat transfer of natural convection in inclined cavities is one of the hot research topics in nonlinear non-equilibrium systems. In this paper, direct numerical simulations of natural convection in an inclined square cavity are carried out by using a high-accuracy numerical method. The effects of the different trends of inclination angle in a range of 0°–180° on the nonlinear evolution of flow field, heat transfer efficiency, and bifurcation are investigated. The Rayleigh number varies in a range from 10³ to 10⁶. The results show that the heat transfer efficiency characterized by Nusselt number is highly dependent on the Rayleigh number, Prandtl number, and the inclination angle. When the Rayleigh number is high, the Nusselt number will have a small jump near the inclination angle in a range of 80°–100°. The evolution of the flow field and temperature field are more complicated at high Rayleigh number. There are one to three vortices of different intensities in the cavity. At low Rayleigh number and inclination angle of the cavity being close to 90°, the flow state is composed mainly of heat conduction state. In addition, it is found that there exist two stable branches of solutions in a range of Rayleigh number (4949, 314721) when the inclination angle is in the interval of (70°, 110°).