An object of the present invention is to provide a highly heat resistant and highly rigid propylene-based polymer having unprecedentedly high stereoregularity. The propylene-based polymer of the present invention satisfies requirements (1) to (4) and preferably requirement (5): (1) an average meso chain length is 800 to 100,000; (2) a MFR is 0.5 to 1,000 g/10 minutes; (3) a ratio of Mw to Mn, Mw/Mn, as measured by GPC is 4.2 to 20; (4) when the ratio of a component which elutes at a temperature of 122° C. or more as measured by temperature rising elution fractionation (TREF) is A % by weight and the melt flow rate of the requirement (2) is B g/10 minutes, 100≥A≥20×EXP(−0.01×B); (5) an amount of a component soluble in n-decane at 23° C. is 0.01 to 2% by weight.