With the economic development in our country, there are more and more international exchanges and communications. Hence, the ability to read, write, and communicate in English is essential and very necessary. In traditional English classroom teaching, teachers are the disseminators of knowledge, whereas students only receive knowledge passively. Due to the limitation of teaching hours and the lack of teaching approaches, it is necessary to make up for the insufficiency in the teaching activities through computer technology and multimedia technology. Abundant teaching approaches can cultivate the independent inquiry ability of students, and the establishment of such an English learning platform is conducive to improving the students’ ability to make full use of the information technology. Through teaching and learning, the students can become the main entity in the English teaching, which can stimulate their enthusiasm and form a good awareness for English learning. In this paper, the radial basis function (hereinafter referred to as RBF for short) algorithm is adopted. Combined with the constructive English teaching method, practical design and construction are carried out by analyzing the concepts, principles, and application strategies of smart classroom teaching in the multimedia background. The practice has proved that the method proposed in this paper is effective and has certain research value and positive significance for the research on English teaching.