Vaccination appears to be one of the effective strategies to control the COVID-19 pandemic. However, the challenge of vaccine hesitancy may lower the uptake rate and affect overall vaccine efficacy. Being a low-risk group in terms of serious consequences of infection, university students may possess low motivation to get vaccinated. Therefore, an expanded Protection Motivation Theory (PMT) incorporating perceived knowledge, adaptive response, and maladaptive response was proposed to investigate the COVID-19 vaccination intention among Taiwanese university students. University students ( = 924; 575 males; mean age = 25.29 years) completed an online survey during January to February 2021. The proposed expanded PMT model was examined using structural equation modeling (SEM). The results showed that perceived knowledge was significantly associated with coping appraisal (standardized coefficient (β) = 0.820; < 0.001), and coping appraisal was significantly associated with adaptive response (β = 0.852; < 0.001), maladaptive response (β = 0.300; < 0.001) and intention (β = 0.533; = 0.009). Moreover, maladaptive response (β = -0.173; = 0.001) but not adaptive response (β = 0.148; = 0.482) was significantly and negatively associated with intention. The present study's results demonstrated a positive path between perceived knowledge, coping appraisal, and intention among university students. Therefore, improving knowledge among this population may increase the intention to uptake the vaccine.