Physical education teachers in colleges and universities have the crucial responsibility of acting as mentors and guides for the healthy growth of students. The work engagement of these teachers affects the quality of higher education personnel training and health education. Based on the job demand-resource model, this study conducted a questionnaire survey on 500 physical education teachers in 20 colleges and universities in Hebei Province, China. The subjects were selected through convenience sampling. Out of the total, 456 valid questionnaires were recovered. The intermediary effect was tested through the AMOS model analysis and the Bootstrap method. The results revealed that the perceived organizational support of the participating physical education teachers in colleges and universities can positively affect their sense of teaching efficacy, which in turn positively affects work engagement and has a partial mediating effect on the relationship between perceived organizational support and work engagement.