The effect of an imposed magnetic field on Rayleigh–Bénard three-dimensional natural convection was investigated numerically. The cubical cavity is heated from below and cooled from above, and the remaining side walls are insulated. The magnetic field is tilted at an angle α about the horizontal. Flow field and heat transfer were predicted for fluid with   and a wide range of governing parameters such as a Rayleigh number between   and 10⁵, a Hartmann number between 0 and 60, and an inclination angle between 0° and 360°. When a magnetic field is applied on a non-conducting fluid within a cubical cavity, whether the natural convection is promoted or damped is found to depend on both the direction and the magnitude of the magnetic field. The average Nusselt number decreased with an increase of the Hartmann number and increased with an increase of the Rayleigh number. The maximum heat transfer rate was observed for  ° and  , while heat transfer was poor for the vertical direction of the magnetic field. The dependence of the promotion or damping efficiency on α and Ha is also discussed in terms of isocontours and isosurfaces in sight of the dynamic and thermal behaviour of the flow.