This paper proposes an algorithm to recognize EEG signals of individuals using a biometric authentication. Research on brain signals shows that each individual has unique brain wave pattern. Electroencephalography signals generated by mental tasks are acquired to extract the distinctive brain signature of an individual. Electroencephalography signals recorded during four biometric tasks, such as relax, read, spell and math activity were acquired from twenty five healthy subjects. We propose an algorithm for recognition of individuals using power spectral density using Recurrent Neural Network and Feed forward Neural Network. The performance of the Recurrent Neural Network is appreciable with an accuracy of 98% for the spell task and 95% for the read task.