A hybrid model, also called a gray-box model, utilizes a black-box and white-box model simultaneously to capture the behaviors of a complex system. When available data are not sufficient to estimate all the model parameters of the white-box model, the hybrid model can provide an improved prediction compared to using only a black-box or white-box model. However, an effective range of the hybrid model, that is, a valid domain, must be known to ensure the accuracy of the model predictions. This study proposes a method to identify the valid domain of a dynamic hybrid model and suggests its application to a dynamic optimization problem. The resulting valid domain can be easily introduced into the dynamic optimization problem by reformulating the valid domain into sets of inequality constraints. Because of the addition of the valid domain constraints, improvement by optimization using the hybrid model is limited compared to the case of unconstrained optimization. To address this issue, an iterative framework of model updates is presented. The proposed methods are applied to a numerical example of a fed-batch bioreactor to demonstrate the efficacy of the methods.