In a process for producing polypropylene comprising polymerizing propylene in the presence of hydrogen and a catalyst system comprising (A) titanium trichloride obtained by reducing titanium tetrachloride with an organoaluminum compound and reacting the reduced solid with an ether represented by the formula:R.sup.1 --O--R.sup.2wherein R.sup.1 and R.sup.2 are defined hereinbefore, and a halogen compound selected from the group consisting of (i) halogen or interhalogen compounds of the formula, X.sup.1 X.sup.2.sub.a (wherein X.sup.1, X.sup.2 and a are defined hereinbefore), (ii) titanium halides, and (iii) organic halogen compounds, simultaneously or successively and (B) an organoaluminum compound, the improvement which comprises supplying ethylene together with propylene to the polymerization system such that the ethylene concentration in the vapor phase of the system based on the total amount of propylene, ethylene and hydrogen in the vapor phase of the system is 0.15 to 1.5 mol % to obtain a propylene-ethylene copolymer having an ethylene content of from 0.1 to 1.0 wt % is disclosed. The propylene-ethylene copolymer is improved in stretchability.