The propylene-based polymer composition includes a specific amount of a propylene-based polymer (A) having a syndiotactic pentad fraction (rrrr fraction) of 85% or more and containing 90 to 100 mol % of a structural unit derived from propylene; a specific amount of a propylene-based copolymer (B) containing 40 to 89 mol % of a structural unit derived from propylene and 11 to 60 mol % of a structural unit derived from an α-olefin and satisfying a specific equation of intrinsic viscosity [η] and MFR; and specific amount(s) of at least one polymer of an olefin-based thermoplastic elastomer (C), a styrene-based elastomer (D), a propylene/ethylene/α-olefin copolymer (E) and an isotactic propylene-based polymer (F), and optionally an ethylene/vinyl acetate copolymer (G) and/or an ethylene-based polymer (H).