We have grown InN films on 3C-SiC (001) substrates with and without cubic GaN underlayers by RF-MBE. It was found that, in the case of direct growth on 3C-SiC (001), hexagonal InN grows with the crystal orientation as hexagonal InN [1-100]//3C-SiC [110], while, in the case of the growth on cubic GaN underlayers, cubic InN grows with the crystal orientation as cubic InN [110]//cubic GaN [110]. Photoluminescence emissions from the cubic and hexagonal InN films were clearly observed at around 0.7 eV.