With the current prevalence of economic globalization, English is still the international language of choice. The definition of cross-cultural: have a full and correct understanding of cultural phenomena, customs, and habits that are different or conflicting with the national culture, and accept and adapt to it with an inclusive attitude on this basis. Therefore, for Chinese universities, the focus is on cultivating highly qualified talents with intercultural communication skills for the country’s economic development. Intercultural communication skills are an important part of students’ language communication skills. China’s business English teaching has also begun to focus on the cultivation of students’ cross-cultural communication skills, but the effect is not satisfactory. In business English teaching, the most important thing is to improve students’ professional competence and business English expertise, and to cultivate foreign language talents with cross-cultural quality and global awareness. Based on the above reasons, this paper proposes a research on the integration of business English teaching and intercultural communication competence cultivation based on intelligent algorithms. First, this paper adopts the literature method to understand the difficulties in traditional business English teaching and the problems in the process of cultivating intercultural communication competence; then, it adopts the inductive-deductive method of intelligent algorithm and action research method to study the mode of cultivating intercultural communication competence and comprehensive experimental research. Finally, after comprehensive analysis, it was concluded that: the number of domestic literature on intercultural communication competence cultivation increased by 11.98%, and the number of literature was generally on the rise; there were significant differences in test results; the experimental students who were satisfied with the cultivation model studied in this paper reached 45.6%. This article attempts to investigate and analyze the needs of English majors for the cultivation of business English intercultural communicative competence, so as to provide a reference for cultivating students’ intercultural communicative competence. The above data fully indicate that the use of contextual teaching method to cultivate intercultural communication skills in business English courses is effective, attracting students’ enjoyment, cultivating their intercultural communication skills, enhancing their understanding of business etiquette, and improving their ability to conduct business conversations. Intercultural communicative competence refers to the ability to communicate when two parties from different cultural backgrounds communicate in the same situation.