  In this paper, we construct a class of non-weight modules over the
affine-Virasoro algebra of type $A_1$ by taking tensor products of a finite
number of irreducible modules $M(\lambda, \alpha, \beta, \gamma)$ with
irreducible highest weight modules $V(\eta, \epsilon, \theta)$. We obtain the
necessary and sufficient conditions for such tensor product modules to be
irreducible, and determine the necessary and sufficient conditions for such two
modules to be isomorphic. We also compare these modules with other known
non-weight modules, showing that these irreducible modules are new.
