Let W(a, b) be the semidirect product Lie algebra of the centerless Virasoro algebra and its module of the intermediate series, where a, b C. In this paper, we first determine all the skew-symmetric biderivations of W(a, b) .Based on the result of biderivations, we give the explicit form of each linear commuting map on W(a, b) .In particular, we find that there exist non-inner biderivations and non-standard linear commuting maps for certain W(a, b) .
Han et al. (Fri,) studied this question.