Let (H, β) be a Hom-Hopf algebra. Recently we introduced the Hom-Yetter-Drinfeld category via Radford biproduct Hom-Hopf algebra, and proved that it is a braided tensor category. Let (H, β, R (or σ)) be a quasitriangular (or cobraided) Hom-Hopf algebra. In this paper, we prove that the category of left (H, β)-Hom-modules (comodules) is a braided tensor subcategory. As a generalization of Radford biproduct Hom-Hopf algebra, we derive necessary and sufficient conditions for R-smash product Hom-algebra and T-smash coproduct Hom-coalgebra to be a Hom-Hopf algebra. At last, two nontrivial examples are given.