Because of the increasing complexity and nonlinearity of industrial processes, nonlinear model predictive control (NMPC) has been rapidly developed owing to its fast response and robustness. However, the complicated optimization process of NMPC limits its application. Hence, this paper proposes an NMPC method that is compatible with nonlinear modeling and concise online control. First, an elastic autoregressive fuzzy neural network (EAFNN) is proposed under reasonable assumptions. The EAFNN exhibits strong parameter identification and structure optimization capabilities because of its autoregressive layer and elastic mechanism. Second, the EAFNN is adaptively simplified into a linear model based on the real-time working condition information during online control. Third, based on a simplified model, NMPC provides an explicit solution without complex optimization procedures. Finally, numerical simulations and roasting process experiments are conducted. Experimental results show that the proposed method exhibits superior control performance and computational complexity compared with other methods, thereby verifying its effectiveness and superiority. The source code for EAFNN-MPC is publicly available at: https://github.com/553318570/EAFNN_MPC.git. •An improved fuzzy neural network is proposed with higher nonlinear representation.•An elastic mechanism is introduced to learn the optimal model structure.•The control are based on a simplified model for reducing computational burden.•The method can stabilize the roasting temperature and handle interference.