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The present invention provides a method of producing a silicon carbide single crystal in which a sublimation raw material (40) being sublimated is re-crystallized to grow a silicon carbide single crystal (60), comprising accommodating the sublimation raw material (40) at one end side in a reaction vessel (10, 12), and placing a seed crystal of a silicon carbide single crystal at another end side in the reaction vessel; and forming a sublimation atmosphere by a first heating means (21) placed at the one end side so as to enable sublimation of the sublimation raw material; forming a re-crystallization atmosphere by a second heating means (20) placed at another end side so that the sublimation raw material being sublimated by the first heating means is re-crystallizable only in the vicinity of the seed crystal of a silicon carbide single crystal, and the sublimation raw material is re-crystallized on the seed crystal of a silicon carbide single crystal, wherein the first heating means (21) and the second heating means (20) are an induction-heatable coil, wherein the silicon carbide single crystal is grown while maintaining the whole growing surface in a convex shape throughout all growth processes, wherein the diameter of the crystal of silicon carbide decreases gradually toward the sublimation raw material throughout all the growth processes. In one aspect, the current value of the induction heating current in the second heating means (20) is decreased continuously or gradually with the increase of the diameter of a growing silicon carbide single crystal (60). In another aspect, if the temperature at one end side accommodating a sublimation raw material (40) is represented by T1 and the temperature at another end side at which a seed crystal of a silicon carbide single crystal (60) is placed is represented by T2, in the reaction vessel, and the temperature of the part adjacent to the inner peripheral side surface part of the reaction vessel at said another end side is represented by T3, then, T3-T2 and T1-T2 increase continuously or gradually.