Under the background of Belt and Road, not only economic cooperation but also humanistic exchanges between countries should be strengthened, which requires that modern college students have strong communication skills in Business English. This paper discusses the model of cultivation and constructs an ICC model containing five aspects: knowledge, attitude, interpretation and association skills, discovery and interaction skills, and education. Based on this model, the course content and teaching methods are designed around four dimensions: attitude, knowledge, skills, and critical cultural awareness. Through the construction of the intercultural communication competence index system to verify the effect of the ICC model on the cultivation of students’ intercultural communication competence, all dimensions show that the effect of the ICC model is more obvious. The results of teaching practice show that the student’s final average score is 66.59, which is 10.27 points higher than the midterm average score, and the significant probability of the t-test using SPSS is p<0.01, which is a significant difference between before and after. The above-analyzed results prove that the ICC model achieved good teaching effects in the application experiment.