  In 2006, Gao and Zeng \cite{GZ} gave the free field realizations of highest
weight modules over a class of extended affine Lie algebras. In the present
paper, applying the technique of localization to those free field realizations,
we construct a class of new weight modules over the extended affine Lie
algebras. We give necessary and sufficient conditions for these modules to be
irreducible. In this way, we construct free field realizations for a class of
simple weight modules with infinite weight multiplicities over the extended
affine Lie algebras.
