A method of producing a silicon carbide single crystal in which a sublimation raw material 40 is accommodated at the side of vessel body 12 in a graphite crucible 10, placing a seed crystal of a silicon carbide single crystal at the side of cover body 11 of the graphite crucible 10, the sublimation raw material 40 is sublimated by a first induction heating coil 21 placed at the side of sublimation raw material 40, a re-crystallization atmosphere is form by a second induction heating coil 20 placed at the side of cover body 11 so that the sublimation raw material 40 sublimated by the first induction heating coil 21 is re-crystallizable only in the vicinity of the seed crystal of a silicon carbide single crystal, and the sublimation raw material 40 is re-crystallized on the seed crystal of a silicon carbide single crystal, and a silicon carbide single crystal 60 is grown while keeping the whole surface of its growth surface in convex shape through the all growth processes. A high quality silicon carbide single crystal with large diameter excellent in dielectric breakdown property, heat resistance, radiation resistance and the like, suitable for electronic and optical devices and the like, and showing no contamination of polycrystals and polymorphs, no defect of micropipes and the like can be produced efficiently without cracking and the like.