In order to improve the practical ability of English in colleges and universities, this paper puts forward the concept of AKEE teaching based on English intercultural communicative competence under the background of integration of industry and education and designs the intercultural teaching mode of college English based on AKEE teaching under this concept, and constructs the teaching quality evaluation index system of the intercultural teaching mode of English in colleges and universities in the light of the teaching content. On this basis, the English intercultural teaching model was constructed based on the entropy weight-TOPSIS method, and the selected indicators were tested for validity using principal component analysis, and the final evaluation results were obtained by calculating the entropy weights. The results show that in the order of comprehensive evaluation, teaching effect>teacher quality>teaching content>teaching resources>teaching quality feedback, with the mean values of 0.811, 0.804, 0.803, 0.799 and 0.798, respectively. Intercultural teaching of English in colleges and universities can improve the teaching effect as well as the quality of teachers.