Background: With the outbreak and spread of the COVID-19 epidemic, online teaching time has been extended continuously. The changes in teaching methods, teaching conditions, and teaching environment have brought great pressure and difficulties in adjustment to teachers, which have led to a series of physical and mental problems such as negativity, lack of confidence, and depression. The long-term accumulation of these problems makes teachers’ turnover intention increasingly serious. Methods: Based on these premises, this study took 449 high school teachers in China as research objects and investigated the relationship between high school teachers’ resilience, job burnout, and turnover intention in the context of the COVID-19 epidemic. Results: The resilience of high school teachers had a significant negative predictive effect on job burnout and turnover intention (r = −0.473, p < 0.05; r = −0.283, p < 0.05), while job burnout had a significant positive predictive effect on turnover intention (r = 0.485, p < 0.05). At the same time, job burnout played a moderating role between resilience and turnover intention (λ = −0.019, p < 0.001). Discussion: This study suggests that society, schools, families, and individuals should adopt various strategies to improve teachers’ adaptability and relieve teachers’ job burnout, so as to solve the practical problem of teachers’ high turnover intention and ensure continuous improvement and healthy development of online teaching.