  Let $\mathcal{B}_r$ be the $(r+1)$-dimensional quotient Lie algebra of the
positive part of the Virasoro algebra $\mathcal{V}$. Irreducible
$\mathcal{B}_r$-modules were used to construct irreducible Whittaker modules in
[MZ2] and irreducible weight modules with infinite dimensional weight spaces
over $\mathcal{V}$ in [LLZ].In the present paper, we construct non-weight
Virasoro modules
  $F(M, \Omega(\lambda,\beta))$ from irreducible $\mathcal{B}_r$-modules $M$
and $(\mathcal{A},\mathcal{V})$-modules $\Omega(\lambda,\beta)$.
  We give necessary and sufficient conditions for the Virasoro module $F(M,
\Omega(\lambda,\beta))$ to be irreducible. Using the weighting functor
introduced by J. Nilsson, we also we also give the isomorphism criterion for
two $F(M, \Omega(\lambda,\beta))$.
