The machine tool industry is an economically important industry in Taiwan. However, due to the limited natural resources in Taiwan, many of the raw materials required for production must be imported. In 2020, COVID-19, the most serious infectious disease in modern times, broke out across the globe. This has had a great impact on the economic and industrial development of various countries and indirectly affected the development of the machine tool industry. The machine tool industry generally is facing shocks and crises. Therefore, this research article mainly discusses a sustainable operation strategy for the machine tool industry during the COVID-19 epidemic period in Taiwan. Firstly, through the literature on dynamic capability theory (DCT) and expert interviews, the relevant dimensions and criteria are summarized. Then, the fuzzy Delphi method (FDM) and the analytic network process (ANP) are integrated to confirm the relevant dimensions and criteria and to sort the criteria. The five dimensions, in order, are integration ability, learning ability, quality improvement, environmental adaptation, and marketing ability. The ten criteria are diversified learning and innovation ability, integration of multiple sources of knowledge, the ability to learn across departments, the ability to adapt to the external environment, marketing strategy ability, organizational learning ability, integration of resources, improved management efficiency, market research ability, and backward integration. Finally, we put forward business strategies for the ranking results and provide relevant research and industry references.