Three-dimensional numerical simulation of thermocapillary flow in a floating half-zone is performed. The effects of rotating magnetic fields (RMF) on thermocapillary flow of semiconductor melt (Pr=0.01) under microgravity are investigated. With increase in the Marangoni number (Ma) from 15 to 75, the melt flow loses stability changing from a steady axisymmetric flow to a three-dimensional steady flow, and then to a three-dimensional oscillatory flow. Due to the excellent electrical conductivity of the semiconductor melt, the induced Lorentz force under RMF with rotating frequency lambda=50 Hz is effective in stirring the melt in the azimuthal direction and suppressing axial convection, which are both effective in returning the thermocapillary flow after the first and second instabilities to a steady axisymmetric flow. (C) 2010 Elsevier B.V. All rights reserved.