A nonlinear Model Predictive Control (MPC) algorithm and its application to a distillation column are described. The algorithm uses a neural model of the process that is linearized online around the current operating point. The algorithm is computationally efficient because the control policy is calculated explicitly without any optimization. The algorithm requires online repetition of a matrix decomposition task and the solution of linear equations. The obtained solution is projected onto the admissible set of constraints imposed on the magnitude and the increment of the manipulated variables. For the distillation column considered, the control accuracy is comparable not only to that obtained in MPC with online linearization and quadratic programming but also to that obtained in nonlinear MPC, which is based on full nonlinear optimization repeated at each sampling instant.