<p>In this paper we develop an inductive method for constructing quadratic Hom-Lie algebras whose twist maps belong to their centroids. We are interested in those Hom-Lie algebras that are not Lie algebras. We prove that such a Hom-Lie algebra has trivial center and, if it is indecomposable, its twist map is nilpotent. Moreover, we show that there exists a maximal ideal containing the kernel and the image of the twist map. Similar to the double extension procedure for ordinary Lie algebras, we develop an inductive method for constructing this kind of quadratic Hom-Lie algebras, and we prove that every indecomposable quadratic Hom-Lie algebra of this kind can be constructed in such a way. As an application, we explain how to obtain (not necessarily indecomposable) quadratic Hom-Lie algebras of this kind from simple Lie algebras of rank greater than one.</p>