Based on the quark model the cross section for the e+ e→Z0 /γ* →Ω++ccc(-Ω)--ccc exclusive process is investigated at the tree level.Compared with the Z0 → Ω-(-Ω)+ decay,our result shows that the Z0 boson favors decaying into charmed baryon pairs.The results are also compared with the calculation of inclusively charmed baryon production.