In the context of rapid social development, education has also faced many challenges in the market. As an important part of higher education, music courses have important value and effect on the cultivation of students’ healthy psychological quality. Correct and effective music teaching can effectively guide students’ music theory knowledge and aesthetic awareness and promote students’ personal future development. However, the learning of theoretical knowledge in music courses is often abstract and boring. In the actual teaching process, problems such as unsatisfactory teaching effect of teachers and low learning interest and enthusiasm of students are often caused by the single teaching mode. Based on numerical analysis and scientific computing, this paper studies the new ideas of college music teaching mode. Under the guidance of scientific educational theory, numerical analysis and scientific calculation are integrated into the teaching of music curriculum theory, and abstract music theory knowledge is concretized to guide students to learn knowledge in a more intuitive way. In the practice of college music teaching mode based on numerical analysis and scientific computing, the method proposed in this paper can effectively improve students’ learning effect and learning enthusiasm. And through the questionnaire survey, it is found that more than 80% of the students are satisfied with this teaching mode, and 62.5% of the students hope to continue to use this teaching mode in the learning process. It is feasible to apply it in practical teaching.