Data-based empirical models, though widely used in process optimization, are restricted to a specific process being modeled. Model migration has been proved to be an effective technique to adapt a base model from a old process to a new but similar process. This paper proposes to apply the flexible Gaussian process regression (GPR) for empirical modeling, and develops a Bayesian method for migrating the CPR model. The migration is conducted by a functional scale-bias correction of the base model, as opposed to the restrictive parametric scale-bias approach. Furthermore, an iterative approach that jointly accomplishes model migration and process optimization is presented. This is in contrast to the conventional "two-step" method whereby an accurate model is developed prior to model-based optimization. A rigorous statistical measure, the expected improvement, is adopted for optimization in the presence of prediction uncertainty. The proposed methodology has been applied to the optimization of a simulated chemical process, and a real catalytic reaction for the epoxidation of trans-stilbene. (C) 2010 Elsevier B.V. All rights reserved.