The control of a continuously operated fermenter at its maximum productivity level gives rise to a difficult control problem as the location of the optimum operating point changes due to the disturbances. In addition, the fermenter exhibits a change in the sign of the steady state gain near the optimum operating point. This study is aimed at developing an on-line optimizing control scheme that can track the changing location of the steady state optimum so as to maximize the fermenter productivity. A nonlinear Laguerre model, whose parameters are estimated on-line, is used for tracking the optimum operating point. The control at the optimum point is achieved using an adaptive nonlinear MPC strategy that uses the nonlinear Laguerre model for prediction. The efficiency of the proposed algorithm is demonstrated by simulating the control of a continuous fermenter that exhibits shift in the location of the optimum operating point in response to the changes in the maximum specific growth rate. The proposed on-line optimizing control strategy is shown to result in a considerable improvement in the closed loop performance even in the presence of measurement noise.