Nonlinear model predictive control (NMPC) has gained widespread attention due to its ability to handle variable bounds and deal with multi-input, multi-output systems. However, it is susceptible to computational delay, especially when the solution time of the nonlinear programming (NLP) problem exceeds the sampling time. In this paper we propose a fast NMPC method based on NLP sensitivity, called advanced-multi-step NMPC (amsNMPC). Two variants of this method are developed, the parallel approach and the serial approach. For the amsNMPC method, NLP problems are solved in background multiple sampling times in advance, and manipulated variables are updated on-line when the actual states are available. We present case studies about a continuous stirred tank reactor (CSTR) and a distillation column to show the performance of amsNMPC. Nominal stability properties are also analyzed. (C) 2013 Elsevier Ltd. All rights reserved.