A solution growth of 3C-SiC was performed on (111)Si-face or )111(C-face of 3C-SiC seed crystal at around 1700 °C by dipping method. The polytype of the crystal grown on the Si-face immediately changed to 6H-SiC. On the other hand, 3C-SiC stably grew on the C-face except for a small number of 6H-SiC precipitates. The polytype transition phenomenon can be explained by the difference of the chemical potential and the solution-crystal interfacial energy between 3C-SiC and 6H-SiC. To grow a larger 3C-SiC crystal, we carried out a long-term growth for 30 hours on the C-face. In the first 10 hours, the polytype of the grown crystal was 3C-SiC. In the next 10 hours, however, the polytype changed from 3C-SiC to 6H-SiC. According to our studies, 6H-SiC tends to grow on 6H-SiC at around 1700 °C, while both of 3C-SiC and 6H-SiC can grow on 3C-SiC at around the same temperature. In this case, 6H-SiC grows on 6H-SiC precipitates and then the dominant polytype changes to 6H-SiC after several 6H-SiC precipitations. To grow 3C-SiC crystal stably, it is necessary to surpress completely the polytype transition by the growth on C-face at lower growth temperatures.