A finite element algorithm is used to analyze the process of floating zone Gystal growth under microgravity. The effect of phase change convection coupled with surface tension convection is considered. The results show that the rate of crystal growth is very important. The single-crystal-melt interface is steeper than the feed-melt interface during the process of crystal growth. When the rate exceeds a critical value, the Marangoni vortex nearby the feed-melt interface will become so large that a secondary vortex exists.