Control performance degradation is a common phenomenon in chemical processes. How to achieve online tuning of controller parameters with few experiments while ensuring the stability and safety of the control system is a significant challenge. In this study, a data-driven controller parameters online tuning method based on model-inherited trust region Bayesian optimization is proposed. First, the objective function and safety constraints of Bayesian optimization for controller online tuning problem are excavated using control performance assessment (CPA) based on time series modeling. Second, utilizing the correlation between local modeling tasks, a model-inherited Gaussian process regression (GPR) method is proposed to build the accurate surrogate model between controller parameters and control performance. This surrogate model consists of two parts: one is the inheritance part of historical GPR models and the other is the residual part interpreted as a zero-mean Gaussian process, so that the model accuracy can be guaranteed with a small amount of evaluation data. Third, a constraint acquisition function based on expected improvement is designed to ensure safe exploration during the tuning procedure, in which feasibility probability of constraints such as overshoot and settling time from CPA are incorporated through a weighted approach. Moreover, a shape-adaptation update method of the trust region is developed to improve optimization efficiency and robustness. Finally, the effectiveness of the method is verified through two industrial cases.