  The purpose of this paper is to determine skew-symmetric biderivations
$\text{Bider}_{\text{s}}(L, V)$ and commuting linear maps $\text{Com}(L, V)$ on
a Hom-Lie algebra $(L,\alpha)$ having their ranges in an $(L,\alpha)$-module
$(V, \rho, \beta)$, which are both closely related to $\text{Cent} (L, V)$, the
centroid of $(V, \rho, \beta)$. Specifically, under appropriate assumptions,
every $\delta\in\text{Bider}_{\text{s}}(L, V)$ is of the form
$\delta(x,y)=\beta^{-1}\gamma([x,y])$ for some $\gamma\in \text{Cent} (L, V)$,
and $\text{Com}(L, V)$ coincides with $\text{Cent} (L, V)$. Besides, we give
the algorithm for describing $\text{Bider}_{\text{s}}(L, V)$ and $\text{Com}(L,
V)$ respectively, and provide several examples.
