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 μ+μ− 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 μ+μ− → Z*/γ* → γγγ at muon colliders. For the muon collider with $$ \sqrt{s} $$ s = 3 TeV and $$ \mathcal{L} $$ L = 1 ab−1, the expected constraints are about two orders of magnitude stronger than those at the 13 TeV LHC.