  Higher-order topological insulators have attracted considerable interests as
a novel topological phase of matter, where topologically non-trivial nature of
bulk protects boundary states whose co-dimension is larger than one. It has
been revealed that the alternating pattern of hopping amplitudes in
two-dimensional lattices provides a promising route to realization of the
higher-order topological insulators. In this paper, we propose that a
honeycomb-lattice model with anti-Kekul\'{e} distortion hosts a higher-order
topological phase. Here, the term anti-Kekul\'{e} distortion means that the
pattern of strong and weak hoppings is opposite to that for the conventional
Kekul\'{e} distortion. We demonstrate the existence of the higher-order
topological phase by calculating the $\mathbb{Z}_6$ Berry phase that serves as
a bulk topological invariant of the higher-order topological phase, and by
showing the existence of corner states.
