This paper proposes a nonlinear model predictive control (NMPC) strategy based on a local model network (LMN) and a heuristic optimization method to solve the control problem for a nonlinear boiler–turbine unit. First, the LMN model of the boiler–turbine unit is identified by using a data-driven modeling method and converted into a time-varying global predictor. Then, the nonlinear constrained optimization problem for the predictive control is solved online by a specially designed immune genetic algorithm (IGA), which calculates the optimal control law at each sampling instant. By introducing an adaptive terminal cost in the objective function and utilizing local fictitious controllers to improve the initial population of IGA, the proposed NMPC can guarantee the system stability while the computational complexity is reduced since a shorter prediction horizon can be adopted. The effectiveness of the proposed NMPC is validated by simulations on a 500 MW coal-fired boiler–turbine unit.