In our previous study, we calculated the transition form factors of J/psi -> D-(s)((*)) using the QCD sum rules. Based on the factorization approximation, the form factors obtained can be applied to evaluate the weak non-leptonic decay rates of J/psi -> D-(s)((*)) + M, where M stands for a light pseudoscalar or vector meson. We predict that the branching ratio for inclusive non-leptonic two-body weak decays of J/psi, which are realized via the spectator mechanism, can be as large as 1.3x10(-8); in particular, the branching ratio of J/psi -> D-s*(+/-) + rho(-/+) can reach 5.3x10(-9). Such values will be marginally accessed by the ability of BESIII, which will begin running very soon.