It is a tremendous opportunity to study the weak rare decay of $J/\psi$ using the largest $J/\psi$ data samples in the world produced by the Beijing Electron Positron Collider (BEPCII) at a center-of-mass energy $\sqrt{s} = 3.097$ GeV and collected with the BESIII detector. In this proceeding, I summarize the BESIII results which have been published in 4 papers of about 6 reaction channels on the weak rare decays of $J/\psi$ in last eight year.