A magnetization force caused by an inhomogeneous magnetic field is a body force and acts on both paramagnetic and diamagnetic fluids. Most practically important fluids are diamagnetic. In this paper, the magnetic effect on natural convection in non-and low-conducting diamagnetic fluids is numerically investigated, focusing on the effects of the direction of magnetization force and the dependence of Ra. The studied fluid is confined in an electrically insulating rectangular cavity and the convection is driven by a horizontal temperature gradient (x-direction). Computations are carried out for non-conducting (Pr = 7.0) and low-conducting (sigma = 15 Omega(-1) m(-1), Pr = 7.0) fluids. When a magnetic field is applied on a non-conducting fluid vertically along the z-direction or horizontally along the x-direction, whether the natural convection is promoted or damped is found to depend on the direction of the magnetization force. As the field is applied horizontally along the y-direction, the natural convection is only weakly promoted. For low-conducting fluids on which both Lorentz and magnetization forces act, the efficiency of damping convection increases, compared with non-conducting fluids, while that of promotion is reduced. For both fluids, the dependence of the promotion or damping efficiency on Ra is also discussed.