University-based entrepreneurship education is facing a paradigm shift between the classical "business school" and the contemporary cross-disciplinary "technology venturing" approach, mainly advocated by engineering schools and other communities outside business schools. The conflict is between structured "business planning and executing" following a tradition of management education, and "opportunity search and exploitation," following Schumpeterian entrepreneurial thought and reflecting the method common to cross-disciplinary discoveries in science, thus reflecting the nature of entrepreneurship. In the latter approach, the entrepreneurship curriculum is built as a platform for the interaction of a variety of disciplines to enhance cross-disciplinary thinking. Based on a comparative analysis of internationally acknowledged entrepreneurship education programmes, this article presents the cross-disciplinary and cross-cultural approach to the technology entrepreneurship curriculum development for undergraduates at Kaunas University of Technology in Lithuania. The method relies on the sequential development of individual, team-based and business skills. These three levels of competence development build the framework for the curriculum design and course didactics, which focus on mixed group work, international curriculum design and teaching, and participation in international innovation challenges. The efficiency of the method was assessed using student entrepreneurial attitude testing (at the start and end of the course) and international student achievement testing (achievements in the international business idea contest). The article offers an insight into the development of a technology-based entrepreneurship curriculum which is relevant to universities in Europe and worldwide.