A process for producing polypropylene is provided which comprises polymerizing propylene in multiple stages, in the presence of a catalyst which is prepared by reacting a first organoaluminum compound (i), or a reaction product (vi) formed between the first organoaluminum compound (i) and an electron donor (a), with titanium tetrachloride (c) to obtain a first solid product (ii), reacting the resulting first solid product (ii) with the electron donor (a) and an electron acceptor (b) to obtain a second solid product (iii), and combining the resulting second solid product (iii) with a second organoaluminum compound (iv) and an aromatic carboxylic acid ester (v) at a molar ratio of the aromatic carboxylic acid ester to the second solid product (v/iii molar ratio) of from 0.1 to 10.0, in such a manner that from 10 to 90% by weight of the total polymer is produced in a first stage and the balance of the total polymer is produced in a second and any subsequent stages with the v/iii molar ratio of the catalyst being made higher in the second and any subsequent stages than that in the catalyst used in the first stage by adding the aromatic carboxylic acid ester (v) to the polymerization system so as to give 1.ltoreq.v/iii molar ratio.ltoreq.10, while controlling the melt flow rate (MFR) of a polymer portion produced in each of the first and any subsequent stages so as to satisfy the relationships:0.5