This paper introduces the characteristics of the course of Linear Algebra and the problems existing in the teaching and learning of the course. In the light of the problems, it proposed to strengthen the construction of the teaching staff, to promote the blended teaching mode, to emphasize the professional application in the teaching process, to integrate ideological and political education into the classroom teaching, to cultivate morality in teaching, and to strengthen the internal drive of students so as to improve the quality of classroom teaching.