To produce an anhydrous magnesium halide solution almost free from calcium from a magnesium halide hydrate containing calcium as an impurity, in addition, prepare a high-activity solid titanium catalyst component for olefin polymerization from the anhydrous magnesium halide solution.

The solution of anhydrous magnesium halide is prepared by adding a potassium compound to the solution to precipitate and remove calcium, when water is distilled off from a solution comprising a magnesium halide hydrate containing at least calcium as an impurity and an oxygen-containing organic solvent to form a solution containing anhydrous magnesium halide and an oxygen-containing organic solvent. The resultant anhydrous magnesium halide solution is brought into contact with a titanium compound in the liquid form to precipitate a solid titanium catalyst component whereby the solid titanium catalyst component for olefin polymerization is prepared.