This paper aims at pointing out the possibility of teaching courses about ethics in general education of Technology University. We deliver the course of ”moral reasoning” to demonstrate the possibility. The distinguishing feature of this course is the combination of the narrative of moral quandary and moral theory. Through the course, we try to lead the students to learn the theories in ethics and enhance their capability of moral reasoning. Through the experience of teaching ethical course and the elucidation the relationship of the course and general education, we find two possibilities of teaching ethics. Firstly, teachers must take account of the particularity of the students of Technology University and lead them to learn the core spirits of general education. Secondly, teachers can adjust their teaching skills to break through the teaching quandary.