  The muon collider has recently received a great deal of attention because of
its ability to achieve both high energy and high luminosity. It plays as a
gauge boson collider because the vector boson scattering (VBS) becomes the
dominant production topology for Standard Model processes starting from a few
TeV of collision energy. In this paper, we propose that the process of
$\mu^+\mu^-$ annihilation into tri-photon is also very sensitive to the search
of anomalous quartic gauge couplings (aQGCs). We investigate the projected
constraints on the transverse operators contributing to aQGCs through
$\mu^+\mu^-\to Z^\ast/\gamma^\ast\to \gamma\gamma\gamma$ at muon colliders. For
the muon collider with $\sqrt{s}=3$ TeV and $\mathcal{L}=1\;{\rm ab}^{-1}$, the
expected constraints are about two orders of magnitude stronger than those at
the 13 TeV LHC.
