Unsteady thermocapillary convection in a rectangular cavity with an upper, deformable free surface has been considered. The unsteady bulk motion is caused by a periodic time-dependent heating along the free surface. The numerical scheme, based on the finite-difference method with a time-dependent boundary-fitted curvilinear coordinate system, has been developed to solve this unsteady thermocapillary free-boundary problem. The influence of the oscillating temperature on the surface deformation and the velocity field is considered. The present computational results are consistent with the previous analytical results in that there exist time lags between the velocity field, surface temperature variation, and surface deformation.