The use of artificial intelligence technology is one of the important focused research areas in the field of education because students need to become aware of the use of automated teaching systems within educational settings. This exploration aims to use the new teaching concept and realize a high-quality teaching effect in quality education. First, the ability-oriented Science, Technology, Engineering, Arts, and Mathematics (STEAM) education is expounded from the four aspects of ability objectives, students, projects, and teaching system construction, and the ability-oriented STEAM graded teaching system is proposed. Second, using the primary school stage as an example, combined with the thinking advanced path of cognitive psychology and the Primary School Science Curriculum Standard of Compulsory Education, a four-dimensional STEAM graded teaching system of “ability, knowledge, project, and evaluation” guided by innovative ability and involved with other abilities is constructed. Third, the shaping path and specific implementation strategies of the system are analysed. Finally, the backpropagation neural network (BPNN) model is used to evaluate the effect of STEAM graded teaching. The results show that the accuracy of students’ answers in the proposed STEAM graded teaching method is significantly higher than that in the traditional teaching method, and the evaluation error of the BPNN model is less than 1%, proving that the BPNN model has good calculation accuracy and can be used to evaluate the effect of STEAM graded teaching. This exploration provides a reference for the practice of STEAM education in China.