  In this paper, we study the representation theory of affine Nappi-Witten Lie
algebra $\widehat{H_4}$ corresponding to the Nappi-Witten Lie algebra $H_4$. We
completely classify all Cartan-free modules of rank one for the Nappi-Witten
Lie algebra $H_4$. With the help of Cartan free $H_4$ modules we classify all
Cartan-free modules of rank one over affine Nappi Witten Lie algebra. We also
give a necessary and sufficient condition for these modules to be irreducible.
Finally as an application we classify Cartan free modules of rank one for
affine-Virasoro Nappi-Witten Lie algebras.
