The teaching of mathematics basic course in newly - built undergraduate colleges is confronted with outstanding problems such as the compression of class time, the decline of students' quality, the waste of teaching resources and the weakening of curriculum objectives. According to the characteristics of new undergraduate colleges, the course should be application-oriented, select teaching content, problem-driven to implement inquiry teaching, build network as a platform to achieve resource sharing, and practice as a link to enhance the application level, in order to comprehensively improve the quality of mathematics basic course teaching.