Discovering proteins with desired functionalities using protein engineering is time-consuming. Offline Model-Based Optimization (MBO) accelerates protein sequence design by exploring the vast protein sequence space using a trained proxy model. However, the proxy model often yields excessively good values that are far from the training dataset and causes pathological behavior in the MBO. To address this problem, we propose a mean deviation tree-structured Parzen estimator (MD-TPE) that penalizes unreliable samples located in the out-of-distribution region using the deviation of the predictive distribution of the Gaussian process (GP) model in the objective function to find the solution in the vicinity of the training data, where the proxy model can reliably predict. Upon examining the GFP dataset, compared to TPE, MD-TPE yielded fewer pathological samples. Additionally, it successfully identified mutants with higher binding affinity in the antibody affinity maturation task. Thus, our developed safe optimization approach is useful for protein engineering.