  In this paper we discuss the structure of the tensor product
V'_{\alpha,\beta}\otimes L(c,h) of irreducible module from intermediate series
and irreducible highest weight module over the Virasoro algebra. We generalize
Zhang's irreducibility criterion, and show that irreducibility depends on the
existence of integral roots of a certain polynomial, induced by a singular
vector in the Verma module V(c,h). A new type of irreducible Vir-module with
infinite-dimensional weight subspaces is found. We show how the existence of
intertwining operator for modules over vertex operator algebra yields
reducibility of V'_{\alpha ,\beta}\otimes L(c,h) which is a completely new
point of view to this problem. As an example, the complete structure of the
tensor product with minimal models c=-22/5 and c=1/2 is presented.
