The invention relates to a method for rapidly growing a large-size high-purity semi-insulating silicon carbide single crystal. According to the method, on one hand, through multiple times of gas replacements conducted on a growing chamber, the insulation of the growing chamber and air is achieved, the nitrogen content in the single crystal is reduced, on the other hand, the rapid-growth of the silicon carbide single crystal is achieved through improving temperature gradient between source powder and a seed crystal in a silicon carbide single crystal growing system of a PVT method and/or reducing pressure of the growing chamber, and the crystal forms of the high-purity semi-insulating silicon carbide single crystal comprise a 4H, 6H, 3C and 15R or an arbitrary combined crystal form of the four crystal forms. The method for rapidly growing the large-size high-purity semi-insulating silicon carbide single crystal has the advantages that resistivity of the silicon carbide single crystal is improved, the growth speed of the silicon carbide single crystal can reach 0.5 mm/h-2 mm/h, the growth speed exceeds the conventional speed for multiple times, and the productive rate of the silicon carbide single crystal is further improved.