  The observed early X-ray plateau in the afterglow lightcurves of some
gamma-ray bursts (GRBs) is attributed to the dipole radiations (DRs) of a
newborn magnetar. A quasi-periodic oscillation (QPO) signal in the plateau
would be strong evidence of the magnetar precession motion. By making a
time-frequency domain analysis for the X-ray afterglow lightcurve of GRB
180620A, we find a QPO signal of $\sim650$ seconds in its early X-ray plateau.
We fit the lightcurve with a magnetar precession model by adopting the Markov
chain Monte Carlo algorithm. The observed lightcurve and the QPO signal are
well represented with our model. The derived magnetic field strength of the
magnetar is $B_{\rm p}= (1.02^{+0.59}_{-0.61})\times10^{15}$~G. It rapidly
spins down with angular velocity evolving as $\Omega_{s} \propto(1+t/\tau_{\rm
sd})^{-0.96}$, where $\tau_{\rm sd}=9430$~s. Its precession velocity evolution
is even faster than $\Omega_s$, i.e. $\Omega_{ p}\propto
(1+t/\tau_{p})^{-2.18\pm0.11}$, where $\tau_{p}=2239\pm206$~s. The inferred
braking index is $n=2.04$. We argue that the extra energy loss via the
magnetospheric processes results in its rapid spin-down, a low braking index of
the magnetar, and the strong precession motion.
