Search for new physics with charm rare decays at BESIII.
The BESIII experiment has collected 2.6 billion $\psi(3686)$ events, 10 billion $J/\psi$ events, $20 fb^{-1}$ D meson pairs at 3.773 GeV, and $7.33 fb^{-1}~D_{s}D_{s}^{*}$ events from 4.128 to 4.226 GeV. The huge data samples allow us to search for rare processes in charm hadron decays. In this paper, we report the FCNC decay in $J/\psi\to D^0\mu^+\mu^-$, $J/\psi\to D^0\gamma$ and $D_{s}^{+}\to h(h')e^+e^-$. The search for $J/\psi$ weak decays containing a D meson, $J/\psi\to D_{s}^{-}\pi^{+}$, and $J/\psi\to D_{s}^{-}\rho^{+}$ will also be presented.