  The Yang-Baxter (YB) deformations of Wess-Zumino-Witten (WZW) model on the
Heisenberg Lie group ($H_4$) are examined. We proceed to obtain the
nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE)
for the $ h_4$ Lie algebra by using its corresponding automorphism
transformation. Then we show that YB deformations of $H_4$ WZW model are
splitted into ten nonequivalent backgrounds including metric and $B$-field such
that some of the metrics of these backgrounds can be transformed to the metric
of $H_{4}$ WZW model while the antisymmetric $B$-fields are changed. The rest
of the deformed metrics have a different isometric group structure than the
$H_{4}$ WZW model metric. As an interesting result, it is shown that all new
integrable backgrounds of the YB deformed $ H_4$ WZW model are conformally
invariant up to two-loop order. In this way, we obtain the general form of the
dilaton fields satisfying the vanishing beta-function equations of the
corresponding $\sigma$-models.
