  The aim of this paper is to define and study Yetter-Drinfeld modules over
weak Hom-Hopf algebras. We show that the category ${}_H{\cal WYD}^H$ of
Yetter-Drinfeld modules with bijective structure maps over weak Hom-Hopf
algebras is a rigid category and a braided monoidal category, and obtain a new
solution of quantum Hom-Yang-Baxter equation. It turns out that, If $H$ is
quasitriangular (respectively, coquasitriangular)weak Hom-Hopf algebras, the
category of modules (respectively, comodules) with bijective structure maps
over $H$ is a braided monoidal subcategory of the category ${}_H{\cal WYD}^H$
of Yetter-Drinfeld modules over weak Hom-Hopf algebras.
