Polydisperse propylene polymer and process for producing the same

A process of producing a polydisperse propylene polymer having a ratio of a weight-average molecular weight to a number-average molecular weight (Mw/Mn) of 4.0 or higher, a melting point (Tm) of 165° C. or lower, and a difference between the melting point (Tm) and a heat distortion temperature (HDT) of 30° C. or less, characterized by polymerizing a propylene monomer or a mixed monomer of propylene and other olefin(s) by a multistage polymerization wherein the polymerization conditions are changed stepwise in the presence of a supported metallocene catalyst having a transition metal compound and an aluminoxane or a reaction product thereof supported on a finely particulate support, and an organoaluminum compound, wherein the transition metal compound is selected from the group consisting of dimethylsilylene(2,3,5-trimethylcyclo-pentadienyl)(2′,4′,5′-trimethylcyclopenta-dienyl) zirconium dichloride, dimethylsilylene bis (2-methyl-4-phenylindenyl)zirconium dichloride and dimethylsilylene bis(2-methyl-4,5-benzoindenyl)zirconium dichloride which may contain the meso form thereof.