  We consider solutions of Kapustin-Witten equation with Nahm pole boundary on
$S^3\times \mathbb{R}^+$. These solutions are usually called Nahm pole
solutions. In this paper, we will prove that there exists a constant $C>0$ such
that $\|F_A\|_{L^2}\leq C$ for any Nahm pole solution $(A,\phi)$.
