A multistage propylene-based polymer including the following components (A) and (B): (A) 5 to 20 wt % of a propylene homopolymer component or a copolymer component of propylene and an .alpha.-olefin with 2 to 8 carbon atoms having an intrinsic viscosity [.eta.] of more than 10 dL/g in tetralin at 135.degree. C.; and (B) 80 to 95 wt % of a propylene homopolymer component or a copolymer component of propylene and an .alpha.-olefin with 2 to 8 carbon atoms having an intrinsic viscosity [.eta.] of 0.5 to 3.0 dL/g in tetralin at 135.degree. C.