the present invention relates to a process for producing a polypropylene - ethylene block copolymer by a continuous multi - stage polymerization comprising a first stage in which polypropylene is polymerized in a first polymerization vessel in the presence of a propylene polymerization catalyst , and a second stage in which propylene and ethylene are copolymerized in a second polymerization vessel , wherein the polypropylene slurry discharged from the first polymerization vessel is supplied to a concentrator to separate said slurry into a concentrated polypropylene slurry and a supernatant liquid , the concentrated polypropylene slurry is then introduced through an upper part of a hydraulic sedimentation classifier to be contacted with a countercurrent of the upward flowing of the supernatant fluid introduced through a lower part of said classifier to obtain hydraulically sedimented polypropylene , and non - hydraulically sedimented polypropylene ; the thus obtained hydraulically - sedimented polypropylene is then supplied to the second polymerization vessel or to a further propylene polymerization vessel and the non - hydraulically sedimented polypropylene is then recycled from the classifier to the first polymerization vessel . the present process produces a propylene - ethylene block copolymer having excellent characteristics of cold shortness and high impact strength .