In this paper, decay widths of the doubly heavy baryons (Ξcc and Ξ bc ) production are theoretically calculated in the whole phase space through W + → Ξcc + c + s and W + → Ξ bc + b + s, within the framework of nonrelativistic QCD (NRQCD). Differential widths dΓ/ds12, dΓ/ds23, dΓ/dcosθ12, and dΓ/dcosθ13 are also given. In addition to the ordinary S-wave contributions for the baryons, we specifically calculate P-wave contributions as a comparison, namely the high excited states of the intermediate diquark, including [ 1 P1] and [ 3 PJ ] (with J = 0, 1, 2) in both color antitriplet state 3 and color sextuplet state 6. It shows that the contribution from the P-wave is about one order lower than the S-wave. According to the results, we can expect plentiful events produced at the LHC, i.e., 3.69 × 10 5 Ξcc events and 4.91 × 10 4 Ξ bc events per year.