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 split 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 σ-models.