A method to globally optimize the parameters of the controller of an inertially stabilized platform is presented. This platform carries an electro-optical system. The quality of the produced image is obviously influenced by the capacity of the controller to compensate for the unwanted motion of the platform. The motion Modulation Transfer Function (motion MTF) measures the amount of blur brought into the image by those parasite movements. The controller is tuned by minimizing a criterion which includes the motion MTF. However, evaluating this criterion is time-consuming. Using an optimization method that needs numerous evaluations of the criterion is not compatible with industrial constraints. Bayesian optimization methods consist in combining prior information about the criterion and previous evaluation results in order to choose efficiently new evaluation points and reach the global minimizer within reasonable time. In this paper, a Bayesian approach is used to optimize the motion MTF-based criterion. The results are compared with a local optimization of the same MTF-based criterion, initialized with an acceptable point. Similar performances are achieved by the proposed methodology, without requiring an initialization point.