A propylene polymer composition includes a propylene homopolymer (A) having an intrinsic viscosity [η] measured in a tetralin solvent at 135° C. in the range of 7 to 12 dl/g, a propylene polymer (B) having an intrinsic viscosity [η] in the range of not less than 0.21 dl/g and less than 0.54 dl/g, and having a proportion of a component eluted at a temperature of not more than −20° C. in TREF in the range of not more than 3.5 mass %, and a propylene polymer (C) having an intrinsic viscosity [η] in the range of not less than 0.54 dl/g and less than 2.6 dl/g, wherein the content of (A) is 0.5 to 47.5 mass %, the content of (B) is 5 to 95 mass % and the content of (C) is 2.5 to 85.5 mass %, based on the total of (A), (B) and (C).