Vietnam has opened her door to embrace globalization; therefore, learning English to communicate is both urgent and vital to contact in the internalization process. However, training leaners, especially at tertiary level, seems to be a daunting task to a great number of Vietnamese teachers of English. According to some research, the reasons for this problem were from the teaching method and their vague understanding of communicative competence. This paper aims to provide an overview of some research on models of training communicative competence and present problems in teaching students to acquire the ability to communicate in English at tertiary level. The authors also suggest a model applicable in training Vietnamese students for their communicative competence. The research may benefit both teachers and educational leaders since it can provide practical information on communicative language teaching and solutions.