  This short note shows the superconvergence of an
$H(\mathrm{grad}\,\mathrm{curl})$-nonconforming brick element very recently
introduced in [17] for the quad-curl problem. The supercloseness is based on
proper modifications for both the interpolation and the discrete formulation,
leading to an $O(h^2)$ superclose order in the discrete
$H(\mathrm{grad}\,\mathrm{curl})$ norm. Moreover, we propose a suitable
postprocessing method to ensure the global superconvergence. Numerical results
verify our theory.
