The aim of this paper is to introduce and study Yetter-Drinfeld category over a weak monoidal Hom-Hopf algebra H. We first show that the category (HWMHYD)-W-H of Yetter-Drinfeld modules over H with a bijective antipode is a braided monoidal category. Secondly, we discuss some properties on the symmetries of the category (HWMHYD)-W-H. Finally, we prove that the representation category of triangular weak monoidal Hom-Hopf algebra is a symmetric braided monoidal subcategory of (HWMHYD)-W-H. Furthermore, a class of weak monoidal Hom-Yetter-Drinfeld modules are constructed by a quasitriangular weak monoidal Hom-Hopf algebra.
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