Education Institution evaluation is one of the most critical activities in teaching and learning process. Selecting the wrong institution could be enough to deteriorate the whole process and operational positions. This paper proposes and demonstrates the application of Data Envelopment Analysis (DEA) in evaluating the performance measures of Indian institute of technology, Chennai and Anna University, Chennai. It was also formulated taking eight Private Deemed universities relative performance efficiency in relation to input and output variable. The result of the paper can be used to identify best educational institute for the purpose of maximizing the contribution to Society.