The first year of college life is the fundamental stage of undergraduate education, and basic general courses (BGC) in which is strictly significant, so the teaching competence of BGC is under intense attention. Based on the learning-centered concept, teaching should directly facilitate learning, and the supply from teachers should match the demand of students. Based on the characteristics of BGC, a framework of teaching competence is established. A questionnaire according to the framework finds that there is a cognition gap between the students and the teachers on teaching competence. The reasons of the deviation were analyzed and the appropriated paths of rectification were discussed.