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Within the Sandard Model, we present the calculation of the branch ratios ofJ/ψsemileptonic weak decay J/ψ→D（s）（*）- +e+νe and J/ψ→D（s）（*）-+M, where Mstand for a light pseudoscalar or vector meson, by means of the instantaneous Bethe-Salpeter method. We first solve the Lorentz covariant Salpeter equation and obtainthe relativistic wave functions of initial and final states, then we use the relativisticwave function to calculate the hadron transition matrix elements of J/ψweak decayprocesses. By approximation, we use the four-Fermi interaction method to give thedecay rate of the semileptonic weak decay, and use several parameters, such as theCKM matrix elements, the full width of J/ψ, which come from the experiments, toget the final results.Based on the hadronic transition matrix elements of J/ψsemileptonic weak de-cay processes, using factorization approximation, to get the color allowed and single-Cabbibo suppressed non-leptonic processes. These non-leptonic results are muchmore bigger than semileptonic ones, so the branch ratios would be detected directly,which already be marginally accessed by the ability of BESIII which is already run-ning now.
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