We propose a new crystal growth method named "the graded solute concentration method" for obtaining homogeneous mixed crystals from their melts in the presence of residual acceleration of the order of 10(-3)-10(-4) G in microgravity. In this method, the feed with preinstalled solute concentration profile is used for compensating solute loss at the solid-liquid (S/L) interface due to convection caused by the residual acceleration. By the preliminary ground-based experiments using capillary tubes with a 1.5 mm bore, we obtained homogeneous In0.4Ga0.6Sb and In0.2Ga0.8Sb crystals. These results show the validity of the proposed method.