In this paper, a turbidostat model with single species for an inhibitory growth-limiting nutrient is considered. The dilution of the turbidostat is controlled by a critical cell concentration in the bioreactor. It is shown that the limit system of the proposed model has a coexistence equilibrium which is global asymptotically stable. Moreover, it is shown that the limit system doesn’t exist limit cycle in the first quadrant. In addition, it presents the discussion of the bioprocess optimization.