  We employ the transport model coupled with hydrodynamic equations to study
the charmonium dissociation and regeneration in the quark-gluon plasma (QGP)
with the large baryon chemical potential in Au-Au collisions at the energies of
$\sqrt{s_{NN}}=$ ($39$, $14.5$, $7.7$) GeV. The baryon chemical potential
$\mu_B$ is encoded in both Debye mass characterizing the heavy-quark potential
and also the equation of state (EoS) of the bulk medium respectively. After
considering $\mu_B$-corrections in both heavy quarkonium and the QGP medium, we
calculate the nuclear modification factor $R_{AA}$ of charmonium. And find the
$\mu_B$ influence on charmonium production at $\sqrt{s_{NN}}$ = 39 and 14.5 GeV
is negligible, while the $R_{AA}$ of charmonium is reduced considering $\mu_B$
influence at $\sqrt{s_{NN}}=7.7$ GeV Au-Au collisions. It is crucial for
studying charmonium production in low energy and also fixed-target heavy-ion
collisions.
