Based on 10 billion $J/\psi$ events accumulated by the BESIII detector, we show the searches for the rare process of $J/\psi$ weak decays. We also search for other rare decay process, such as the FCNC process $D^0\to\pi^0\nu\bar{\nu}$. Using $J/\psi$ decay, BESIII also produce millions of Hyperon, which can be used to search for the rare decay process $\Xi^-\to\Xi^0 e\nu$.