The observed matter-antimatter asymmetry in the universe composes a serious challenge to our understanding of nature. BNV/LNV 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 $J/\psi\to\Lambda_c^+e^-+c.c.$ is searched, and no signal event is observed. The upper limit of the branching fraction is set to be $6.9\times10^{-8}$ at $90\%$ Confidence Level, which is still much higher than the estimation based on SM. For the process with $\Delta B=2$, a search for $\Lambda$-$\bar\Lambda$ oscillation is performed for the first time. No evidence of the baryon oscillation is observed, the upper limit for the rate of $\bar\Lambda$ oscillates to $\Lambda$ is determined
as $\mathcal{P}(\Lambda)=\frac{\mathcal{B}(J/\psi\to pK^-\Lambda+c.c.)}
{\mathcal{B}(J/\psi\to pK^-\bar\Lambda+c.c.)}<4.4\times10^{-6}$, and the oscillation parameter $\delta m_{\Lambda\bar\Lambda}$ is calculated to be less than $3.8\times10^{-15}$ MeV at 90\% confidence level.