The purpose of this paper is to determine skew-symmetric biderivations Bider s (L,V ) and commuting linear maps Com(L,V ) on a Hom-Lie algebra (L, α) having their ranges in an (L, α)-module (V, ρ, β ), which are both closely related to Cent(L,V ), the centroid of (V, ρ, β ). Specifically, under appropriate assumptions, every δ ∈ Bider s (L,V ) is of the form δ (x, y) = β −1 γ([x, y]) for some γ ∈ Cent(L,V ), and Com(L,V ) coincides with Cent(L,V ). Besides, we give the algorithm for describing Bider s (L,V ) and Com(L,V ) respectively, and provide several examples.