We study inclusive production of doubly heavy baryon at a collider and at hadron colliders through fragmentation. We study the production by factorizing nonpertubative- and perturbative effects. In our approach the production can be thought as a two-step process: A pair of heavy quarks can be produced perturbatively and then the pair is transformed into the baryon. The transformation is nonperturbative. Since a heavy quark moves with a small velocity in the baryon in its rest frame, we can use NRQCD to describe the transformation and perform a systematic expansion in the small velocity. At the leading order we find that the baryon can be formed from two states of the heavy-quark pair, one state is with the pair in 3S1 state and in color -3, another is with the pair in 1S0 state and in color 6. Two matrix elements are defined for the transformation from the two states, their perturbative coefficients in the contribution to the cross-section at a collider and to the function of heavy quark fragmentation are calculated. Our approach is different than previous approaches where only the pair in 3S1 state and in color -3 is taken into account. Numerical results for e+e− colliders at the two B-factories and for hadronic colliders LHC and Tevatron are given.