  The supermassive black hole (SMBH) with 4 millions solar mass inside the
radio-source Sgr A* in our Galactic center is the nearest SMBH. Once the S
stars with shorter period are observed, the relativistic precessions especially
the Lense-Thirring one can be measured by astronomical observations at 10
micro-arcsecond ($\mu$as) level in future. An interesting but so far no
attended problem is that the SMBH has not only spin but also spin precession
like the other objects in the universe. In this paper, we study the effect of
such spin precession on the orbital precessions of orbiting stars. Our results
show that the spin precession can produce a periodic oscillation on the
precession of the star's orbital plane, but no obvious effect on the periapse
shift. For stars with $O(0.1)$yr period, such visible oscillations occur while
the SMBH's spin-precession period is about from few tens of years to hundreds
of years. And the period of oscillation is the same with the one of the spin
precession. In principle, this oscillating orbital plane's precession can be
observed and then the spin and spin precession of the nearest supermassive
black hole can be determined.
