  The discovery of radio pulsars (PSRs) around the supermassive black hole
(SMBH) in our Galactic Center (GC), Sagittarius A* (Sgr A*), will have
significant implications for tests of gravity. In this paper, we predict
restrictions on the parameters of the Yukawa gravity by timing a pulsar around
Sgr A* with a variety of orbital parameters. Based on a realistic timing
accuracy of the times of arrival (TOAs), $\sigma_{\rm TOA}=100\,\mu{\rm s}$,
and using a number of 960 TOAs in a 20-yr observation, our numerical
simulations show that the PSR-SMBH system will improve current tests of the
Yukawa gravity when the range of the Yukawa interaction varies between
$10^{1}$-$10^{4}\,{\rm AU}$, and it can limit the graviton mass to be $m_g
\lesssim 10^{-24}\,{\rm eV}/c^2$.
