PURPOSE: To obtain the subject polymer having a reduced content of extractive substances in hexane at a good efficiency by polymerizing ethylene in the presence of a catalyst containing an organoaluminum compound and a TiCl3 component prepared by reducing TiCl4 with a metal having a high reduction potential.

CONSTITUTION: The objective polymer having a reduced content of extractive substances in hexane is obtained by polymerizing ethylene in the presence of a catalyst comprising (A) an organoaluminum component (e.g. triethylaluminum or the like) and (B) a titanium trichloride component prepared by reducing titanium tetrachloride with a metal (e.g. zinc or the like) having a reduction potential higher than -1.5 V by treating the titanium tetrachloride in an electron donor solvent (an alkyl ester of a saturated carboxylic acid or the like) with a sufficient amount of such metal to reduce the titanium tetrachloride to titanium trichloride and to produce an insoluble chloride of such metal, removing the insoluble chloride by filtration, adding magnesium chloride to the resulting solution to produce a catalyst component having an Mg/Ti ratio of 1:1 to 56:1, and impregnating a suitable support with the obtained solution.