In this paper we consider all orientation-preserving Z4-actions on 3-dimensional handlebodies Vg of genus g>0. We study the graph of groups (Γ(v),G(v)), which determines a handlebody orbifold V(Γ(v),G(v))≃Vg/Z4. This algebraic characterization is used to enumerate the total number of Z4 group actions on such handlebodies, up to equivalence.