The present invention provides a method of growing silicon single crystals by the Czochralski method, wherein the strength of a neck may be increased so as to delete the risk of severance thereof in a simple and easy way without the use of mechanically complex devices and thereby growing of a single crystal of a larger diameter and heavy weight is made practically possible. The method comprises the steps of: a single crystal being so grown from a seed crystal that the diameter of said single crystal gets gradually narrower until the length of a seed taper reaches 2.5 to 15 times the sectional size of the seed crystal; the diameter of a long near-cylindrical neck following the seed taper being so regulated that said diameter may be 0.09 to 0.9 times the sectional size of the seed crystal and 2.5 mm as the smallest in diameter; the spread of the diameter fluctuation of the neck being so restricted as to be less than 1 mm; and the length of the neck being so controlled as to be kept within the range of 200 mm to 600 mm.
