Data Envelopment Analysis (DEA) is a mathematical programming model used to evaluate the relative efficiency of decision-making units (DMUs) and has been widely applied in the field of management decision-making. Traditional cross-efficiency DEA methods heavily rely on accurate and precise data. When data uncertainty exists, the DEA model solution obtained under deterministic assumptions may lose feasibility, making the efficiency evaluation results unreliable. To address this issue, this paper proposes a robust cross-efficiency DEA model based on the robust optimization. To mitigate the issue of non-unique cross-efficiency values caused by multiple optimal solutions, a secondary objective model is established to select a set of acceptable optimal solutions. In addition, the study introduces the concept of the price of robustness to analyze the ability of DMUs to cope with data uncertainty and discusses the choice between the benevolent and aggressive strategies. Finally, the feasibility and effectiveness of the proposed method are validated using the renewable energy data from 15 OECD countries.