A method to synthesize graphene materials using a DC high current divergent plasma torch has been developed. Carbon atoms were generated by the decomposition of propane-butane, methane and acetylene in a thermal plasma jet. The graphene materials were characterized by electron microscopy, thermogravimetry, Raman spectroscopy. The influence of the experimental conditions on the morphology and phase composition of the synthesis products was investigated. The optimal conditions for the synthesis of high-purity graphene flakes have been found.