We investigate the possibilities of growing a uniform binary compound crystal in space numerically, proposing a new crystal growth method. We develop a numerical calculation method of the growth of binary crystals, in which convection induced by temperature and concentration differences in the solution is taken into account. How to determine the shape and movement of the solution-crystal interface during the crystal growth is clearly explained for binary crystals, which is more complicated than that for single-component crystals. The boundary fit method is employed to solve this moving boundary phase transition problem. The calculation method is applied to the crystal growth analysis of an InAs-GaAs binary semiconductor and the effect of buoyancy convection induced under microgravity conditions on the crystal growth process is investigated. We found that the concentration field is disturbed and, as a result, the solution-crystal interface is deformed by buoyancy convection even when the gravitational acceleration is as low as 10-6 g, which is supposed to be the gravity level in the International Space Station. We also found that the direction of residual gravity has a strong effect on the concentration field in the solution and the crystal growth process. Next, we analyse the influence of g-jitters and the Sorét effect on the crystal growth process. We, in fact, found that g-jitters and the Sorét effect have little influence on the macroscopic crystal growth process. The dependence of the generation of supercooling in the solution on convection is also investigated. We found that supercooling is not induced by convection if residual gravity is 10-6 g. Finally, the possibility of growing high quality InGaAs crystals of uniform compositions in space is discussed.