Culture and language are closely related.Culture tends to be the essential factor for the successful communication.Hence, promoting intercultural communicative competence will be the ultimate aim in EFL teaching.The potential intercultural communicative problems are discussed in this paper, including inappropriate language transfer, misunderstanding of nonverbal communication, different value systems and improper teaching techniques, and then some effective strategies to promote intercultural communicative competence are put forward, such as, revealing words cultural meaning, finding discourses cultural information, creating communications situational and cultural context and applying communication strategies.Of course, many approaches are applied to language teaching and learning, which will shift the focus of attention from the linguistic forms to communicative competence.The teacher would expose his students to the target culture as much and often as possible, and help them to achieve the higher intercultural awareness and communicative competence.