A propylene polymer composition comprising the following components (A), (B), and (C) and satisfying the requirements to : Component (A): a propylene polymer comprising a structural unit derived from propylene in an amount of 90% by weight or more when the total weight of the propylene polymer is 100% by weight; Component (B): at least one elastomer selected from the group consisting of (B1) an ethylene-α-olefin copolymer having a structural unit derived from ethylene in an amount of more than 10% by weight and 99% by weight or less when the total weight of the ethylene-α-olefin copolymer is 100% by weight and a structural unit derived from an α-olefin having 3 to 10 carbon atoms and (B2) a hydrogenated conjugated diene polymer; Component (C): a propylene block copolymer comprising a propylene polymerization block (I) having a structural unit derived from propylene in an amount of 90% by weight or more when the total weight of the propylene polymerization block is 100% by weight and at least one elastomer block (II) selected from the group consisting of (II-1) an ethylene-α-olefin copolymer block having a structural unit derived from ethylene in an amount of more than 10% by weight and 99% by weight or less when the total weight of the ethylene-α-olefin copolymer block is 100% by weight and a structural unit derived from an α-olefin having 3 to 10 carbon atoms and (II-2) a hydrogenated conjugated diene polymer block; Requirement : the propylene polymer composition has a melting point of 100°C or more; Requirement : the propylene polymer composition has a limiting viscosity of 1.0 dl/g or more; Requirement : at least one of the number-average molecular weight of a component insoluble in p-xylene at 25°C of the propylene polymer composition and the number-average molecular weight of a component insoluble in n-heptane at 25°C of the propylene polymer composition is 80000 or more; and Requirement : the ratio of the polystyrene-equivalent number-average molecular weight of the component (A) to the polystyrene-equivalent number-average molecular weight of the component (B) is 1.0 or more and 20 or less, wherein the content of the component (C) is 60% by weight to 99.9% by weight when the total weight of the propylene polymer composition is 100% by weight. Component (A): a propylene polymer comprising a structural unit derived from propylene in an amount of 90% by weight or more when the total weight of the propylene polymer is 100% by weight; Component (B): at least one elastomer selected from the group consisting of (B1) an ethylene-α-olefin copolymer having a structural unit derived from ethylene in an amount of more than 10% by weight and 99% by weight or less when the total weight of the ethylene-α-olefin copolymer is 100% by weight and a structural unit derived from an α-olefin having 3 to 10 carbon atoms and (B2) a hydrogenated conjugated diene polymer; Component (C): a propylene block copolymer comprising Requirement : the propylene polymer composition has a melting point of 100°C or more; Requirement : the propylene polymer composition has a limiting viscosity of 1.0 dl/g or more; Requirement : at least one of the number-average molecular weight of a component insoluble in p-xylene at 25°C of the propylene polymer composition and the number-average molecular weight of a component insoluble in n-heptane at 25°C of the propylene polymer composition is 80000 or more; and Requirement : the ratio of the polystyrene-equivalent number-average molecular weight of the component (A) to the polystyrene-equivalent number-average molecular weight of the component (B) is 1.0 or more and 20 or less, <EOS>