In the Indian context, an academic study program at the Indian Institutes of Technology (IITs) comprises a mixed group of learners coming from various social-economic, education, and a wide range of linguistic backgrounds. These learners secure admission into various engineering programs at IITs, having qualified for the Joint Entrance Exam (JEE), a national-level competitive exam. To qualify for this exam, students prepare rigorously, even at the school level. The JEE exam tests students’ knowledge in the core subjects such as Physics, Chemistry, Mathematics, Aptitude and Reasoning; hence, students seem to focus more on these core subjects but not on the English language. These learners vary widely in their English language proficiency level in terms of oral and written English proficiency. It is believed that the level of language proficiency of learners has a direct influence on their academic performance in the program in which they are admitted. Therefore, the study aims at diagnosing 405 engineering students’ competence of English language skills at the entry-level undergraduate engineering study programs of Bachelor of Technology at the Indian Institute of Technology, Bhubaneswar. A diagnostic test that comprised the components of English language skills was designed and administered to 405 students. The results were analyzed and interpreted qualitatively and quantitatively. It was found that the majority of the students who performed well in the test had better education backgrounds. For the students who performed poorly, the study recommends possible implications besides some remedial measures.