The use of human brain electroencephalography (EEG) signals for automatic person identification has been investigated for a decade. It has been found that the performance of an EEG-based person identification system highly depends on what feature to be extracted from multi-channel EEG signals. Linear methods such as Power Spectral Density and Autoregressive Model have been used to extract EEG features. However these methods assumed that EEG signals are stationary. In fact, EEG signals are complex, non-linear, non-stationary, and random in nature. In addition, other factors such as brain condition or human characteristics may have impacts on the performance, however these factors have not been investigated and evaluated in previous studies. It has been found in the literature that entropy is used to measure the randomness of non-linear time series data. Entropy is also used to measure the level of chaos of brain computer interface systems. Therefore, this thesis proposes to study the role of entropy in non-linear analysis of EEG signals to discover new features for EEG-based person identification. Five different entropy methods including Shannon Entropy, Approximate Entropy, Sample Entropy, Spectral Entropy, and Conditional Entropy have been proposed to extract entropy features that are used to evaluate the performance of EEG-based person identification systems and the impacts of epilepsy, alcohol, age and gender characteristics on these systems. Experiments were performed on the Australian EEG and Alcoholism datasets. Experimental results have shown that, in most cases, the proposed entropy features yield very fast person identification, yet with compatible accuracy because the feature dimension is low. In real life security operation, timely response is critical. The experimental results have also shown that epilepsy, alcohol, age and gender characteristics have impacts on the EEG-based person identification systems.