  Let $(H,\a_H)$ be a Hom-Hopf algebra, $(A,\a_A)$ a right $H$-comodule algebra
and $(C,\a_C)$ a left $H$-module coalgebra. Then we have the category
$_A\mathcal{M}(H)^C$ of Hom-type Doi-Hopf modules. The aim of this paper is to
make the category $_A\mathcal{M}(H)^C$ into a braided monoidal category. Our
construction unifies quasitriangular and coquasitriangular Hom-Hopf algebras
and Hom-Yetter-Drinfeld modules. We study tensor identities for monoidal
categories of Hom-type Doi-Hopf modules. Finally we show that the category
$_A\mathcal{M}(H)^C$ is isomorphic to $A\#C^*$-module category.
