In the classroom teaching of Chinese international education (CIE), teachers will face different types of problems. Teachers should focus on each teaching link, identify key and difficult points, teach students in line with their aptitude, and emphasize communication with students to improve the classroom teaching quality in CIE. The classroom teaching quality evaluation of CIE in higher-education institutions is regarded as multiple-attribute decision-making (MADM). Recently, the EDAS and CRITIC model was employed to put forward the MADM. The double-valued neutrosophic sets (DVNSs) are employed as the optimal decision tool for expressing the uncertain data during the classroom teaching quality evaluation of CIE in higher-education institutions. In this paper, EDAS is founded for MADM under DVNSs. Then, the double-valued neutrosophic number EDAS (DVNN-EDAS) model is constructed for MADM. Finally, a numerical example for classroom teaching quality evaluation of CIE is employed to verify the DVNN-EDAS model. The main decision contribution of this study is that (1) the novel MADM technique is established in line with EDAS and CRITIC under DVNSs. (2) The objective weights are constructed through CRITIC. (3) A numerical example for classroom teaching quality evaluation of CIE in higher-education institutions in line with the DVNN-EDAS is constructed.