A Galerkin finite element method, together with the boundary conformal mapping technique, is used to investigate the change of melt/crystal interface under low gravity during the growth of LICAF system. Results have shown that strong convection can cause a deeply concave interface toward the crystal, and significantly increase radial thermal gradients near the interface. The flow intensity and the change of the gravity have a linear relationship under low gravity (g0=10-2-10-6). At small Ma number, the maximum acceleration for keeping a planar growth interface is gmax=1×10-3g under our given conditions. In addition, the growth velocity may have some influence on the growth interface shape even at μg gravity level, indicating that the growth velocity cannot be too fast even when convection is very weak.