A class of parameter-dependent dynamic control policies is explored for its use in a model predictive control (MPC) algorithm for a nonlinear system modeled with a feedforward neural network (NN). The NN-modeled system is expressed as a polytopic quasi-linear-parameter-varying (quasi-LPV) system over a region of the state-input space for a range of operating points, and the dynamics of the proposed policy, which are optimized off-line to enlarge the region of attraction, are allowed to depend on a time-varying parameter of the polytopic quasi-LPV system model such that the resulting control involves a continuous gain-scheduling that leads to reduced conservativeness. A complete MPC algorithm using the dynamic policy as the terminal policy ensures stabilization and improved control performance over a larger domain of attraction without a larger horizon length. Simulation examples with tank and tubular reactor systems illustrate the effective performance of the proposed approach in practical applications. (C) 2015 Elsevier Ltd. All rights reserved.