The natural convection heat transfer of electrically non-conducting fluids can be controlled by gradient magnetic field. The gradient magnetic fields with different profiles of magnetic field intensity were set up by various configurations of neodymium-iron-boron permanent magnet system. The magnetic field intensities and magnetic accelerations for differently configured gradient magnetic fields were obtained by numerical simulation. The natural convection heat transfer of air in a two-dimensional enclosure that was placed in different gradient magnetic fields was numerically investigated. The flow and temperature fields for the air natural convection were presented and the local and mean Nusselt numbers on the walls were calculated and compared. The results showed that the natural convection heat transfer of air can be enhanced or controlled by applying permanent gradient magnetic fields with different magnetic accelerations.