Abstract: To control the conditions of groimg crystal and to restrain Marangoni convections in the melt caused by weak gravity is puzzles when growing excellent crystal in the microgravity condi-tion. However,solving all of these problems by the way of testing, not only to spond high economic invest and long test time,but also sometime it is very difficulty for us to truly simulate by means of experiment.It is a important researching branch of growing crystal in space to simulate convection process in the melt hi the microgravity condition by numerical simulatIOn,calculating result has guiding significant for controlling the growth condition of crystal in space and for restraining convection in the melt.The results of numerical research about convection to occur and evolve in the melt are described and the convection process in the horizontal zone of the hielt, upper which there are free surface and different boundary conditions have ben studied by the finite difference method.