Marangoni convection is a flow along the interface between two fluids due to the variation of surface tension, which is mainly caused by temperature and/or concentration gradients, namely thermal and/or solutal Marangoni convection(s). During the crystal growth by the floating zone method, Marangoni convection may induce the striation and affect the quality of growing crystal. Therefore, it is necessary to understand the convective phenomenon and control it. In this study, a three-dimensional configuration of the half-zone liquid bridge in the crystal growth of Si x Ge 1-x was selected by establishing the temperature and concentration differences. The equations of continuity, momentum, energy and mass transfer were solved by the PISO algorithm in the OpenFOAM. Thermal and solutal Marangoni convections were set to flow in the opposite direction under zero gravity in the melt with different Marangoni numbers. Results have shown that when Ma C is larger than −Ma T , the flow is steady and axisymmetric, while Ma C is smaller than −Ma T , the flow is unsteady and irregular. As for the control of Marangoni convection, rotation of top and bottom plane in the liquid bridge was applied during the crystal growth. With different rotation speeds and directions, the suppression of Marangoni convection can be effectively realized by the appropriate forced rotation.