A mathematical model of two competitive populations with migrations between two patches in manufacturing engineering is proposed. It is assumed that migration rates of the two populations are not constants but density-dependent which are led mainly by the pressure from interspecific competition. Conditions for the persistence of the system are obtained which shows that appropriate migration rates facilitate the two competitive populations to cooperate well such that both the populations are persistent in every patch. The results are confirmed by computer simulations. It is also found that the positive equilibrium which is globally stable changes into bitable equilibrium as the parameters vary.