Objective Various factors may influence the attitudes of medical students towards euthanasia, including personal values, beliefs, and personality traits. The objective of this study was to examine the attitudes of second and fifth year medical students about euthanasia and the relationship with students’ personality traits. Methods Medical students from the Universities of Kragujevac and Belgrade participated in this study. A questionnaire assessed attitudes toward euthanasia and student personality traits (honesty–humility, emotionality, extraversion, agreeableness, conscientiousness, and openness [HEXACO-60]). Results More than 50% of students in the second year and 60% of students in the fifth year were supportive of euthanasia. Students in the fifth year were 2.5 times more likely to express a concern that euthanasia needs to be clearly regulated by law compared to students in the second year. The adjusted analyses indicated that lower levels of honesty–humility and emotionality were positively associated with students’ belief that euthanasia should be legalized. Conclusion Many medical students in Serbia have a positive attitude towards euthanasia. It is important to consider the possible influences of culture, religion, and the law on attitudes towards euthanasia. Undergraduate medical training should include more hours dedicated to palliative care and end-of-life topics to raise awareness of patients’ preferences in this regard.