We study the base sizes of finite quasiprimitive permutation groups of twisted wreath type, which are precisely the finite permutation groups with a unique minimal normal subgroup that is also non-abelian, non-simple and regular. Every permutation group of twisted wreath type is permutation isomorphic to a twisted wreath product G = T :P acting on its base group Ω = T , where T is some non-abelian simple group and P is some group acting transitively on k = {1, . . . , k} with k > 2. We prove… Expand