The observed matter-antimatter asymmetry in the universe composes a serious challenge to our understanding of nature. BNV decay has been searched in many experiments to understand this large-scale observed fact. In the case of e+e- collision, few experiments are performed. Here we proposed to search BNV and LNV with currently the world largest J/psi data sets in e+e- collision experiment. The BNV and LNV channel J/psi -> Lambda_c+ e- +c.c. is studied, and no signal event is observed. The upper limit branching fraction is set to be 6.910E-8 at 90% C.L., which is still much higher than the estimation based on SM. The Majorana neutrino is searched in LNV decays D-> (K-pi-/Kspi-/K-pi0) e+e+ and no significant signal is observed, the upper limits on the branching fractions are set to be 2.710E-6, 3.310E-6 and 8.510E-6 at 90% C.L., respectively. The Majorana neutrino is also investigated with different mass assumption, ranging from 0.25 to 1.0 GeV/c^2 in the decays D0 -> K-e+nu_N(pi-e+) and D+->Kse+nu_N(pi-e+), and the upper limits on the branching fractions are extracted to be at the level of 10E-7 to 10^-6 at 90% C.L..