Biometric person identification is getting more effective and popular because of Electroencephalography (EEG). EEG signals can be captured from human scalp invasively or non-invasively with the help of electrodes. EEG-based biometric system is more secure and unique for person identification. In this paper, we have used two different states to explore the adaptive and uniqueness of the EEG-based biometric system. We have used Eyes Open (EO) state as well as Eyes Closed (EC) state of a EEG motor imagery publicly available dataset of 109 users.The model is trained and tested with EO and EC states alternatively to prove the reliability and robustness of the model. The biometric person identification model has been designed using Support Vector machine (SVM) for classification. We achieved a notable person identification rate of 96% (EO) and 91.78% (EC) using SVM with Radial Basis Function (RBF) kernel. We have also used Ensemble Support Vector Machine (ESVM) to enhance the performance of person identification and observed the average performance accuracy of 96.16% with n number of classifier.