The use of multistage evaporators, motivated by the energy economy from reusing the flashed steam is common in a wide range of process industries. Such evaporators however present several control problems which manifest in the form of strong interactions among the many process variables, significant dead times, tendency to open-loop instability and severe nonlinearities. In this paper, a nonlinear model predictive control (NMPC) scheme utilizing a proportional-integral (PI) controller in its inner loop is developed for a simulated industrial-scale five-stage evaporator using a continuous-time recurrent neural network in state space as its internal model. Input-output data obtained from closed-loop system identification experiments are used in training the network by the Levenberg-Marquardt algorithm with automatic differentiation. A similar approach is used in developing an optimal control law for the plant based on the model predictions. The effectiveness of this scheme is tested by simulating various control problem scenarios involving set-point tracking and disturbance rejection and comparing performance with that of decentralized PI controllers developed earlier. Results show significant improvements in control performance, particularly in terms of settling time.