Abstract Background COVID-19 has resulted in more than 670 million confirmed cases and more than 6.8 million deaths worldwide as of March 2023. This pandemic situation has put a significant strain on health care systems in each country, and the crises experienced by the USA, Britain and Italy have shown that even developed countries’ systems can collapse. This this study aims to measure and evaluate the performance of OECD countries’ health care systems against COVID-19 in terms of relative efficiency. Methods This study uses DEA to measure and compare the relative efficiency of national health care systems in response to COVID-19. We calculate technical, pure technical, scale, and super efficiency ranks based on the CCR, BCC, and Super-SBM models. The input variables are COVID-19-related health expenses, ICUs, facilities and equipment, and the number of examiners, and the output variable is the excess mortality rate due to COVID-19 of 2020, one year. Results According to the CCR model, two of the 20 analyzed countries, including Denmark and Iceland, are 100% efficient, and the remaining 18 countries are relatively inefficient. The average of technological efficiency is 0.26. According to the BCC model, a total of 10 countries are 100% efficient. The average of pure technical efficiency is 0.71. As a result of measuring the efficiency of scale, Denmark and Iceland are 100% efficient, and the remaining 18 countries are relatively inefficient. The average scale efficiency is 0.28. The super-efficiency ranking was followed by Denmark, Iceland, Korea and, etc. Conclusions When the analysis results were classified by health security system again, efficiency was high in the order of NHS, NHI, and SHI. When classified by financing sources and service provider, it was confirmed that tax-type countries were more efficient than insurance-type countries, and public supply-oriented countries were more efficient than private supply-oriented countries. Key messages • The efficiency of health care system of OECD countries against COVID-19 was measured, and the causes of performance were explored in terms of the structure of the system. • Through this, we intend to derive policy implications that can maintain the sustainability of the health care system in the face of health security crises such as the pandemic.