Numerical computations were carried out for theromagnetic convection of air in a square enclosure under both magnetising and gravitational fields. Scalar magnetic potential method was used to calculate magnetic field. The governing equations in primitive variables were discretized by the finite-volume method and solved by the SIMPLE algorithm. 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 show that the magnetic force has significant effect on the flow field and heat transfer in a square enclosure, the average Nusselt number respects the trend of decrease first and then increase when the magnetic force number increases.