A polydisperse propylene polymer characterized by being produced by polymerizing a propylene monomer or a mixed monomer of propylene and other olefin(s) by a multistage polymerization wherein the polymerization conditions are stepwise changed 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 as a scavenger, and by 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.