Numerical solutions of ordinary differential equations (ODEs) are a basic course for undergraduates majoring in science, technology, engineering and mathematics. Due to the limitation of credit hours, there are many problems in this course, such as abstract theoretical content, insufficient practical training, and disconnection between theory and practical application. Based on the results-oriented education, the principle of construction consistency, cognitive load theory and Bloom’s classification theory of educational objectives, this paper constructs an integrated teaching framework for senior undergraduates. The framework arranges the low-level cognitive task as self-learning before online class. Classroom teaching focuses on the cultivation of high-level analytical ability, and designs a three-level progressive project experimental system to guide students to gradually complete knowledge understanding, code implementation and problem solving. The course reconstructs the teaching content around the three-dimensional training goal of knowledge, ability and literacy, and focuses on the core idea of numerical algorithm and program implementation method. After a semester of teaching practice, students’ understanding of the core concepts of the course is more solid, their ability in algorithm programming and mathematical modeling is significantly improved, and their interest in applied mathematics is also enhanced. This teaching framework has good generality and can provide a reference for the teaching reform of computational mathematics courses at home and abroad.