For a, b ∈ C, the Lie algebra W(a, b) is the semidirect product of the Witt algebra and a module of the intermediate series. In this paper, all biderivations of W(a, b) are determined. Surprisingly, these Lie algebras have symmetric (and skewsymmetric) non-inner biderivations. As an applications, commutative post-Lie algebra structures on W(a, b) are obtained.