  The potential of the muon colliders open up new possibilities for the
exploration of new physics beyond the Standard Model. It is worthwhile to
investigate whether muon colliders are suitable for studying gluonic quartic
gauge couplings~(gQGCs), which can be contributed by dimension-8 operators in
the framework of the Standard Model effective field theory, and are intensively
studied recently. In this paper, we study the sensitivity of the process
$\mu^+\mu^-\to j j \nu\bar{\nu}$ to gQGCs. Our result indicate that the muon
colliders with c.m. energies larger than $4\;{\rm TeV}$ can be more sensitive
to gQGCs than the Large Hadron Collider.
