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In this paper, we obtain a class of Virasoro modules by taking tensorproducts of the irreducible Virasoro modules $\Omega(\lambda,\alpha,h)$ and$\Omega(\mu, b)$ with irreducible highest weight modules $V(\theta,h)$ or withirreducible Virasoro modules Ind$_{\theta}(N)$ defined in [MZ2]. We obtain thenecessary and sufficient conditions for such tensor product modules to beirreducible, and determine the necessary and sufficient conditions for two ofthem to be isomorphic. We also compare these modules with other knownnon-weight Virasoro modules.

New irreducible tensor product modules for the Virasoro algebra (II)