In a process for producing a propylene homopolymer or copolymer which comprises polymerizing propylene or copolymerizing propylene and at least one other unsaturated hydrocarbon monomer in liquid propylene using a catalyst comprising activated titanium trichloride and an organo-aluminum compound, the activated titanium trichloride being prepared by reducing titanium tetrachloride with an organo-aluminum compound followed by activation, introducing the polymer slurry produced into the top of a counter-current washing tower, and washing the slurry by bringing the slurry into counter-current contact with liquid propylene which is introduced into the bottom of the washing tower, the improvement which comprises refining the homopolymer or copolymer of propylene by feeding (a) an alcohol having 3 to 8 carbon atoms in a molar amount of about 0.1 to about 10 times the molar amount of the organo-aluminum compound in the slurry, or (b) a mixture of an alcohol having 3 to 8 carbon atoms and an epoxide, the molar amount of the alcohol being about 0.1 to about 10 times the molar amount of the organo-aluminum compound in the slurry and the molar amount of the epoxide compound being about 0.1 to about 3 times the molar amount of the organo-aluminum compound in the slurry, to a part of the washing tower, thereby simultaneously deactivating the catalyst and removing the catalyst and the propylene homopolymer or copolymer dissolved in the polymer slurry.