  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 irreducibles
defined in [Q. Chen, J. Han, Non-weight modules over the affine-Virasoro
algebra of type $A_1$, J. Math. Phys. 60, 071707 (2019)] with irreducible
highest weight modules. The irreducibility and the isomorphism classes of these
modules are determined. Moreover, we show that these tensor product modules are
different from the known non-weight modules. Finally, we realize some tensor
product modules as induced modules from modules over certain subalgebras of the
affine-Virasoro algebra of type $A_1$, and give sufficient and necessary
conditions for these induced modules to be reducible.
