COVID-19 poses great challenges for preschool teachers in China, which will increase the level of job stress and job burnout, and have an impact on the relationship between job stress, job burnout, and perceived organizational support (POS). However, few studies have examined trilateral relationships, especially the role of POS concerning job stress and job burnout of preschool teachers. This study aimed to investigate the relationship among the three variables of job burnout, job stress, and POS, as well as explore the moderating effects of POS between job stress and job burnout. A cross-sectional study was conducted among preschool teachers in six provinces of China. A total of 408 preschool teachers completed a self-report questionnaire, including three scales that measured job burnout, job stress, and POS respectively. The Pearson correlation coefficient and regression analysis were used to examine the relationship among variables. The results showed that job burnout among Chinese preschool teachers was at a medium level during the COVID-19 pandemic. Job stress was positively related to job burnout, and the POS was negatively related to job burnout. Additionally, POS moderated the relationship between job stress and job burnout and alleviated the adverse effects of job stress on the job burnout of preschool teachers. POS can play a moderating role between job stress and job burnout of Chinese preschool teachers during the COVID-19 pandemic.