Usually, parents and caregivers are the ones responsible for children's vaccination, their intention to vaccinate children depending on many factors. In a society where almost half of adults have refused to take a jab against COVID-19, it is important to know which factors increase or decrease the odds of a child getting vaccinated. In the present study, we examined parents’ reasons for/against children vaccination and predictors of this intention. We found that about 30% of parents intended to have their children vaccinated to protect the health of children and their close ones. On the other hand, parents who did not intend to have their children vaccinated were typically afraid of long-term consequences of vaccination and its side effects, with less than one fifth of them being skeptical about vaccination per se. Using logistic regression analyses, we found that a higher willingness to vaccinate was in male, older parents, and those with higher (socio)economic status. Parents with a higher adherence to restrictions, and higher trust in government and authorities were more likely to vaccinate their children. Moreover, parents who had themselves been vaccinated or were more positive towards vaccination in general were much more willing to vaccinate their children. On the contrary, belief in conspiracy theories decreased this intention 10-times. No other variables (e.g., demographic characteristics, mental health indicators, or direct experience with COVID-19) significantly predicted parents’ intention to vaccinate their children. The study offers several implications related to the complexity of factors which determine hesitant parents’ intention to vaccinate their children. We aimed to answer questions on how, when, and by whom parents should be approached to improve their awareness on vaccination decisions.