The melt flow in a Czochralski system with radiative cooling from the melt surface under a horizontal magnetic field was studied by transient three-dimensional numerical computation. A quite peculiar convection mode was obtained under the present magnetic field. Velocity components were all downwards in a vertical cross-section parallel to the magnetic field, while those in a plane perpendicular to the magnetic field were natural convection dominant. A top view of temperature contours represented an elliptic shape which was supported by a practically grown crystal rod with an elliptic cross-section.