The objective of this paper is to present a modified structure and a training algorithm of the recurrent Elman neural network which makes it possible to explicitly take into account the time-delay of the process and a Model Predictive Control (MPC) algorithm for such a network. In MPC the predicted output trajectory is repeatedly linearized on-line along the future input trajectory, which leads to a quadratic optimization problem, nonlinear optimization is not necessary. A strongly nonlinear benchmark process (a simulated neutralization reactor) is considered to show advantages of the modified Elman neural network and the discussed MPC algorithm. The modified neural model is more precise and has a lower number of parameters in comparison with the classical Elman structure. The discussed MPC algorithm with on-line linearization gives similar trajectories as MPC with nonlinear optimization repeated at each sampling instant.