With the advancement of globalization, China is implementing the “Belt and Road Initiative”, a major strategic initiative to open up to the outside world, which means that it needs to cultivate talents with cross-cultural communication skills. In this paper, we design a computer-assisted model for cross-cultural English teaching implementation that is based on the objectives of cross-cultural teaching. A questionnaire was designed to collect data on the effect of students’ communicative competence training in cross-cultural English teaching, and t-tests and correlation tests were used to analyze the impact of the computer-assisted English teaching mode on students’ communicative competence training. The results of the study show that there is a significant difference between the dimensions of intercultural communicative competence of the experimental group of students applying the computer-assisted teaching mode and the control group under traditional teaching at the end of the teaching experiment (P0), indicating that computer-assisted English language teaching can improve students’ intercultural communicative competence. This paper puts forward the optimization suggestions of communicative competence training from the aspects of teaching object and teaching design in order to improve teachers’ professional teaching ability and students’ intercultural communicative competence.