A process for producing a propylene/ethylene block copolymer with a satisfactory morphology, which comprises using a catalyst system comprising (1) a metallocene catalyst giving a highly crystalline polypropylene, (2) a metallocene catalyst giving a lowly crystalline polypropylene, (3) a porous support, and (4) an aluminoxane or a compound capable of forming an ionic complex upon reaction with either of the metallocene catalysts, and optionally containing (5) an organoaluminum compound; and a propylene/ethylene block copolymer obtained by the process. The copolymer is highly transparent and has a low modulus.