This study on level of communicative competence covering linguistic/grammatical and discourse has aimed at constructing a proposed English language program for 5 key universities in Vietnam. The descriptive method utilized was scientifically employed with comparative techniques and correlational analysis. The researcher treated the surveyed data through frequency counts, means and percentage computations, and analysis of variance/t-test to compare two main area variables. The respondents was 221 students from 5 universities randomly chosen. The major findings of the study generally reveal that the students' level of communicative competence is a factor of their parents' academic influence. Their linguistic/grammatical and discourse competence is helped by their chance for formal and intensive learning, conversing with a native speaker of the English language, rich exposure to social media networks, and reading materials written in English. Moreover, the students' greatest strength along linguistic competence is on the use and function of noun, pronoun and preposition, while their weaknesses are on the use and function of conjunction, adverb, interjection, and verb. It is a general finding that the 4th year students who are linguistically competent on the whole system and structure of a language or of languages in general (consisting of syntax, morphology, inflections, phonology and semantics) have the tendency to speak or write authoritatively about a topic or to engage in conversation. Basing on the findings from this study, an enhancement program was proposed with the certainty that this proposed English language program would bring the best efficiency in the second language acquisition.