The floating zone technique is a promising containerless method to realize larger and high-quality crystals of semiconductors under microgravity. Thermocapillary convection, which is caused by the presence of unbalanced surface tension in floating zone, is important for mass and heat transport in crystal growth and is studied with half-zone liquid bridge model in present paper. The free surface of liquid bridge is idealized as non-deformable and adiabatic from the environmental gas. The three dimensional oscillatory thermocapillary flow is investigated numerically by directly solving incompressible Navier-Stokes, energy and continuity equations with finite volume method. The surface tension is added directly in Navier-Stokes equations. The relationship between Marangoni number Ma and dimensionless frequency f*=fH2κ-1 and also flow structures are studied.