PURPOSE: To produce polypropylene excellent in stiffness, moldability, etc., by polymerizing propylene in the presence of a catalyst comprising a solid catalyst component, an organoaluminum compd., a specific methoxysilane compd., and a specific ethoxysilane compd.

CONSTITUTION: A catalyst is prepd. by combining a solid catalyst component contg. at least Mg, Cl, an arom. carboxylic ester (e.g. ethyl benzoate), and Ti, an organoaluminum compd. (e.g. trimethylaluminum), a methoxysilane compd. of formula I, and an ethoxysilane compd. of formula II. In those formulae, R1 and R3 are each a branched alicyclic or arom. hydrocarbon group; R2 and R4 are each a 1-3C linear hydrocarbon group; 0<t≤2 and 0≤Ss≤2 provided 1≤ft≤2; and 0<x≤2 and 0≤y<2 provided 1≤x+y≤2. The catalyst is used to polymerize propylene to produce polypropylene.