In this study, we designed a structural model to determine the relationships among push–pull factors, institutional situations, and satisfaction during the COVID-19 pandemic. The 17 selected indicators fell under five domains, namely push factors, pull factors, institutional leadership, international strategies, and satisfaction. Structural equation modeling (SEM) was used to verify the assumptions of the model. Based on 1005 degree-seeking international students’ views, this study found that push and pull factors may coincidentally exist, and their functions can be modified by institutional situations. The findings suggested pull factors will, through institutional leadership, impact students’ satisfaction, while push factors will not. Moreover, the detection of institutional mediation can provide useful information for specific institutes to develop their future recruiting or retaining strategies. These findings enriched our knowledge of the field for higher education sustainable development. For future studies, this design may be useful to interpret the phenomena of global student mobility in higher education settings.