We search for the lepton-flavor-violating decay of the $J/psi$ into an electron and a muon using $(225.3pm2.8)times 10^{6}$ $J/psi$ events collected with the BESIII detector at the BEPCII collider. Four candidate events are found in the signal region, consistent with background expectations. An upper limit on the branching fraction of $mathcal{B}(J/psi to emu)< 1.5 times 10^{-7}$ (90% C.L.) is obtained.