In this study, we propose a contextual Bayesian optimization with Trust-Region (CBOTR), an extended version of Bayesian optimization (BO) that can find an optimum input of a target system (or unknown function) through the iterative learning and sampling procedure. CBOTR adds two features to BO: (1) CBOTR can take into account context information which modifies the input and output relationship of a target system, and (2) CBOTR restricts the searching space for the next input to be selected so that it can rapidly find an optimum. The results from simulation studies using a set of benchmark functions and a wind farm power simulator showed that the CBOTR algorithm can achieve an almost optimum target value by taking a small number of trial actions (samplings). The proposed algorithm particularly suits well to determine the joint optimal operational conditions of wind turbines in a wind farm for maximizing the total energy production, in that the complex interaction among wind turbines in a wind farm is difficult to model using an analytical model and one needs to find the optimum operational conditions for varying wind conditions.