The goal of this paper is to establish singular Adams type inequality for biharmonic operator on Heisenberg group. As an application, we establish the existence of a solution to
$$\Delta_{\mathbb{H}^n}^2 u=\frac{f(\xi,u)}{\rho(\xi)^a}\,\,\text{ in}\Omega,\,\, u|_{\partial\Omega}=0=\left.\frac{\partial u}{\partial\nu}\right|_{\partial\Omega},$$
where
\({0\in \Omega \subseteq \mathbb{H}^4}\) is a bounded domain,
\(0 \leq a \leq Q,\,(Q=10).\) The special feature of this problem is that it contains an exponential nonlinearity and singular potential.