In this work, we present the use of Kernel Extreme Learning Machine (Kernel ELM) on electroencephalography EEG brain signals in order to classify the P300 wave during the subject development an oddball paradigm. Also, we propose a selection criteria in order to improve the classification accuracy. In this study, the brain signals of healthy and disabled subjects which suffered a stroke were recorded, analyzed and classified. The results reported that the best classification accuracy and average bitrate were 100% using target by block evaluation and 18.38 bits per minute, respectively. These results are compared to various machine learning algorithms so that our results outperformed them.