This study examines 1630 tertiary students in regard to their entrepreneurial career intentions (ECIs) and their influencing factors. The findings may serve as academic reference for the development of entrepreneurship-related education. The results show that students' computer self-efficacy (CSE) has a significant direct effect on ECIs, and entrepreneurship cognition (EC) has a significant effect on ECIs via CSE. The pattern and empirical data of EC and CSE on ECI have a good fit. This paper provides insights from Taiwan's tertiary institutions about the ECIs of students and contributes to a better understanding of them. We describe the development of the influencing factors, discuss the implications and provide suggestions for entrepreneurship education development.