In the thermal CVD method for processing of thin film, a complicated thermal-flow field based on natural convection is formed under the thermal gradient in the reactor, and this thermal-flow field prevents uniform growth on the substrate. As a means to control the natural convection in the reactor, the effect of the gradient magnetic field in a super-conducting magnet was numerically studied on the natural convection of paramagnetic fluid as the first step of research. The fluid is contained in a vertical cylindrical enclosure, which is cooled from both above and side isothermally. The lower end-plate has an isothermally heated disk in the center, while the outer part is thermally insulated. The magnetic field is replaced with that generated by the steady electric current circulating within a single circular electric coil. When the magnetic center is placed below the heated disk, convection is rapidly induced by the magnetic force. The heat transfer rate becomes almost twice that of gravitational natural convection for the conditions studied herein. In contrast, when the magnetic center is placed at either the central height of the enclosure or the upper end plate, the magnetic force rather suppresses the natural convection.