  In Einstein-Gauss-Bonnet gravity, we study the quasi-normal modes (QNMs) of
the tensor perturbation for the so-called Maeda-Dadhich black hole which
locally has a topology $\mathcal{M}^n \simeq M^4 \times \mathcal{K}^{n-4}$. Our
discussion is based on the tensor perturbation equation derived
in~\cite{Cao:2021sty}, where the Kodama-Ishibashi gauge invariant formalism for
Einstein gravity theory has been generalized to the Einstein-Gauss-Bonnet
gravity theory. With the help of characteristic tensors for the constant
curvature space $\mathcal{K}^{n-4}$, we investigate the effect of extra
dimensions and obtain the scalar equation in four dimensional spacetime, which
is quite different from the Klein-Gordon equation. Using the asymptotic
iteration method and the numerical integration method with the Kumaresan-Tufts
frequency extraction method, we numerically calculate the QNM frequencies. In
our setups, characteristic frequencies depend on six distinct factors. They are
the spacetime dimension $n$, the Gauss-Bonnet coupling constant $\alpha$, the
black hole mass parameter $\mu$, the black hole charge parameter $q$, and two
``quantum numbers" $l$, $\gamma$. Without loss of generality, the impact of
each parameter on the characteristic frequencies is investigated while fixing
other five parameters. Interestingly, the dimension of compactification part
has no significant impact on the lifetime of QNMs.
