  In continuation of our recent work about smash product Hom-Hopf algebras in
\cite{MLY}, we introduce Hom-Yetter-Drinfeld category $_H^H{\mathbb{YD}}$ via
Radford biproduct Hom-Hopf algebra, and prove that the Hom-Yetter-Drinfeld
modules can provide solutions of the Hom-Yang-Baxter equation and
$_H^H{\mathbb{YD}}$ is a pre-braided tensor category, where $(H, \b, S)$ is a
Hom-Hopf algebra. Furthermore, we obtain that $(A^{\natural}_{\diamond} H,\a\o
\b)$ is a Radford biproduct Hom-Hopf algebra if and only if $(A,\a)$ is a Hopf
algebra in the category $_H^H{\mathbb{YD}}$. At last, some examples and
applications are given.
