In the CZ process using a cooling member surrounding a single crystal, the cooling member is permitted to effectively serve to increase a pulling speed. Cracks of the single crystal due to excessive cooling are prevented to occur. A high crystal quality is acquired. In order to realize these objects, the temperature of the inner peripheral surface of the cooling member 6 opposing to the outer peripheral surface of the single crystal 4 is restricted to 500° C. or below, even in the lower end, the temperature of which becomes the highest. To achieve this restriction, the thickness T of the cooling member 5 is 10 to 50 mm. The height H of the cooling member 6 is 0.1 to 1.5 times the diameter D of the single crystal 4.