A thermoplastic elastomer composition comprising: (A-1) a crosslinked ethylene copolymer comprising monomer units derived from ethylene and monomer units derived from at least one selected from the group consisting of propylene and α-olefins having 4 to 10 carbon atoms, a propylene polymer comprising monomer units derived from propylene and having a content of the monomer units derived from propylene of greater than 50% by weight, where the whole amount of the component is taken as 100% by weight, a mineral oil, an inorganic filler having an average particle diameter of less than 1.0 μm, wherein, the content of the component (A-1) is 10 parts by weight to 70 parts by weight, the content of the component is 5 parts by weight to 50 parts by weight, and the content of the component is 0 parts by weight to 60 parts by weight, relative to 100 parts by weight of the total amount of the components (A-1),, and, the ratio of the total weight of the components (A-1) and to the weight of the component, {(the weight of the component (A-1)) + (the weight of the component)}/(the weight of the component), is 1 to 19, the content of the component is 10% by weight to 23% by weight relative to 100% by weight of the whole amount of the thermoplastic elastomer composition, the component (A-1) is a crosslinked ethylene copolymer comprising 50% by weight to 95% by weight of monomer units derived from ethylene, and 5% by weight to 50% by weight of monomer units derived from at least one selected from the group consisting of propylene and α-olefins having 4 to 10 carbon atoms, where the total amount of the monomer units derived from ethylene and the monomer units derived from the at least one selected from the group consisting of propylene and α-olefins having 4 to 10 carbon atoms is taken as 100% by weight, and the average particle diameter of the inorganic filler is to be determined as follows: Twenty particles of an inorganic filler are to be observed with a scanning electron microscope, and the area S of a two-dimensional image of each of the particles is to be measured; each of the areas S is considered to be equal to the area of a circle, and the areas S is to be substituted to the following formula R = 2 × S / π 1 / 2 and an arithmetic average of the Rs calculated is to be taken as the average particle diameter of the inorganic filler. (A-1) a crosslinked ethylene copolymer comprising monomer units derived from ethylene and monomer units derived from at least one selected from the group consisting of propylene and α-olefins having 4 to 10 carbon atoms, a propylene polymer comprising monomer units derived from propylene and having a content of the monomer units derived from propylene of greater than 50% by weight, where the whole amount of the component is taken as 100% by weight, a mineral oil, an inorganic filler having an average particle diameter of less than 1.0 μm, wherein, Twenty particles of an inorganic filler are to be observed with a scanning electron microscope, and the area S of a two-dimensional image of each of the particles is to be measured; each of the areas S is considered to be equal to the area of a circle, and the areas S is to be substituted to the following formula R = 2 × S / π 1 / 2 and an arithmetic average of the Rs calculated is to be taken as the average particle diameter of the inorganic filler.