A method is disclosed with provides stable growth of SiC single crystals, particularly 4H—SiC single crystals, with an effective crystal growth rate for a prolonged time even at a low temperature range of 2000° C. or lower. A raw material containing Si, Ti and Ni is charged into a crucible made of graphite and heat-melted to obtain a solvent. At the same time, C is dissolved out from the crucible into the solvent to obtain a melt. A SiC seed crystal substrate is then brought into contact with the melt such that SiC is supersaturated in the melt in the vicinity of the surface of the SiC seed crystal substrate, thereby allowing growth and production of an SiC single crystal on the SiC seed crystal substrate.