The magnetic fields produced by electrical coils are designed for damping the the thermocapillary convection in a floating half-zone in microgravity. The fields are designed specially to reduce the flow near the free surface and then in the melt zone by adjusting the longitudinal coil positions close to the melt zone. The effects of the designed magnetic fields on reducing the flow velocity and temperature distribution non-uniformity in the melt zone are stronger than those of the case of an uniform longitudinal magnetic field obtained by numerical simulation, particularly at the melt-rod interface. It brings fundamental insights into the heat and mass transfer control at the solidification interface by the magnetic field design for crystal growth by the floating full-zone method.