Brown (1994) states, language is a part of culture and culture is a part of language. English language, therefore, has obviously been a bridge for cross-cultural communication thanks to its being worldwide lingua franca. It is recommended that cultivating intercultural competence (IC) should be a special concern in the English language teaching (ELT) curriculum generally and English classrooms thorough Vietnam, especially tertiary contexts. This study aims to utilize an adaption of Newton’s (2016) strategies for enriching IC to develop the IC of Vietnamese English-major students. In addition, the model of Intercultural Communication Competence (ICC) developed by Byram (1997) and Hartmann and Ditfurth (2007) was employed to examine the practice of students’ IC achievement. Thirty-eight Vietnamese tertiary English-major freshmen at Can Tho University were involved in this eight-week program. Data were collected through various IC activities, recorded by class observations, students’ reflections on each activity, and evaluation of students by a questionnaire. The findings revealed that the participants experienced positive gains in knowledge and attitudes toward IC activities, while practical skills in cultural interaction and critical awareness was less enhanced due to limited time for practice. Students’ lack of ICC motivation indicated that the lecturer/researcher should plan more carefully, provide gradual supports.