Purposes: To explore the associated factors of COVID-19 vaccine hesitancy and examine psychometric properties of the coronavirus-related health literacy questionnaire (HLS-COVID-Q22) and Oxford COVID-19 Vaccine Hesitancy questionnaire. Methods: An online survey was conducted from 23 June to 16 July 2021 on 387 school principals across Taiwan. Data collection included socio-demographic characteristics, information related to work, physical and mental health, COVID-19 related perceptions, sense of coherence, coronavirus-related health literacy, and vaccine hesitancy. Principal component analysis, correlation analysis, linear regression models were used for validating HLS-COVID-Q22, Oxford COVID-19 Vaccine Hesitancy, and examining the associations. Results: HLS-COVID-Q22 and Oxford COVID-19 Vaccine Hesitancy were found with satisfactory construct validity (items loaded on one component with factor loading values range 0.57 to 0.81, and 0.51 to 0.78), satisfactory convergent validity (item-scale correlations range 0.60 to 0.79, and 0.65 to 0.74), high internal consistency (Cronbach’s alpha = 0.96 and 0.90), and without floor or ceiling effects (percentages of possibly lowest score and highest score <15%), respectively. Low scores of vaccine hesitancy were found in male principals (regression coefficient, B, −0.69; 95% confidence interval, 95%CI, −1.29, −0.10; p = 0.023), principals with better well-being (B, −0.25; 95%CI, −0.47, −0.03; p = 0.029), and higher HLS-COVID-Q22 (B, −1.22; 95%CI, −1.89, −0.54; p < 0.001). Conclusions: HLS-COVID-Q22 and Oxford COVID-19 Vaccine Hesitancy were valid and reliable tools. Male principals and those with better well-being, and higher health literacy had a lower level of vaccine hesitancy. Improving principals’ health literacy and well-being is suggested to be a strategic approach to increase vaccine acceptance for themselves, their staff, and students.