This action research study aims to test the feasibility of applying an intercultural language learning and teaching model (IcLLT) to teaching EFL in general education in Vietnam through teachers’ and students’ responses to two trial lessons. The IcLLT model of “construction”, “connection”, “interaction”, “reflection”, and “extension” is developed to foster students’ intercultural competence by invoking their engagement in social interaction and critical cultural reflection. As shown in observations and students’ evaluation sheets, the intercultural language activities in IcLLT lessons could engage the students in activating prior knowledge, comparing culture, talking about cultural issues, and participating in intercultural communication. However, they were not able to reflect on their intercultural perspectives in oral interaction as much as in their writing. In parallel, the teacher agreed that the activities requiring students’ reflection were most challenging and the other three steps of “construction”, “connection”, “interaction” could be conducted in relevance to three-stage Communicative Language Teaching (CLT) skill lessons of Pre-While-Post. The IcLLT is applicable to teach integrated skill CLT lessons with culture-specific input if intercultural objectives are added and relevant intercultural language activities with more focus on students’ intercultural interactions and critical reflection are conducted. Hence, IcLLT could be recommended as a supplementary approach to integrating culture into EFL teaching to build students’ intercultural communicative competence, which is considered a critical part of the new educational reform in general education in Vietnam