Based on a modification of a magnetohydrodynamic turbulence model, a numerical study was performed to investigate the effects of transverse uniform and gradient magnetic field on the turbulent flow and heat transfer characteristics of a low melting point molten salt in a stainless steel pipe. With the Hartmann number from 0 to 80, the numerical results showed that the fluid flow displayed anisotropic distributions under the magnetic field with decrease of velocity in the mainstream region, and decrease of turbulent intensity, whereas the flow velocity increased in the boundary layer near the Hartmann and Roberts wall. Especially, a velocity jet phenomenon was observed in the Roberts boundary layers at higher Hartmann number in the uniform magnetic field or the positive gradient magnetic field. Under the gradient magnetic field, the flow and heat transfer of molten salt displayed much more variations than under the uniform magnetic field. The magnetohydrodynamic calculation results proposed here might be helpful to the design of the composite heat transfer system for molten salt in actual industrial applications.