Many processes in the chemical industry have modest nonlinearities, i.e. linear dynamics play a dominant role in governing the process output behaviour in the operating range of interest, but the linearization errors may be significant. For this type of processes, linear-based control may yield a poor performance, while nonlinear-based control results in computation complexity. We propose to model this type of process with a composite model consisting of a linear model (LM) and a multilayered feedforward neural network (MFNN). The LM is used to capture the linear dynamics, while the MFNN is employed to predict the LM's residual errors, i.e., the process nonlinearities. Effective off-line and on-line algorithms are proposed for the identification of the composite model. With this model structure, it is shown that a simple analytical predictive control law can be formulated to control a nonlinear process. Simulation examples are also given to illustrate the effectiveness of the model identification and the proposed predictive control.