  We study the axial gravitational quasinormal modes of a self-dual black hole
in loop quantum gravity. Considering the axial perturbation of the background
spacetime, we obtain the Schr\"{o}dinger-like master equation. Then we
calculate the quasinormal frequencies with the Wentzel-Kramers-Brillouin
approximation and the asymptotic iteration method. We also investigate the
numerical evolution of an initial wave packet on the self-dual black hole
spacetime. We find the quantum correction parameter $P$ positively affects the
absolute values of both the real and imaginary parts of quasinormal
frequencies. We derive the relation between the parameters of the circular null
geodesics and quasinormal frequencies in the eikonal limit for the self-dual
black hole, and numerically verify this relation.
