The main purpose of this paper is to give an explicit formula of a homology cobordism invariant of plumbed homology 3-spheres which was defined in a joint work with M. Furuta by using the Seiberg-Witten monopole equation on 4-dimensional V-manifolds [8]. This formula provides a sufficient condition for homology 3-spheres of plumbing type to have infinite order in the homology cobordism group.