A thermoplastic elastomer composition having at least one elastomer component selected from the group consisting of elastomeric polymers (A) each of which has a side chain (a) containing a hydrogen-bond cross-linkable moiety having a carbonyl-containing group and/or a nitrogen-containing heterocycle and has a glass-transition point of 25° C. or below, and elastomeric polymers (B) each of which contains a hydrogen-bond cross-linkable moiety and a covalent-bond cross-linking moiety in a side chain and has a glass-transition point of 25° C. or below; and a clay, wherein an amount of the clay contained is 20 parts by mass or less relative to 100 parts by mass of the elastomer component.