Abstract : A Brain-Computer Interface (BCI) is a communication system designed to allow the users who suffering from totally paralysis to send messages or commands without sending them through the brains normal output pathway. The overall objective of this project is to design and implement an algorithm that could separate and classify task-related Electroencephalography (EEG) signal from ongoing EEG signals. The task is the movement of right or left index finger. The separation was made by using the Independent Component Analysis (ICA), neurocomputing algorithm which transforms the observed EEG signals across all channels into mutually independent components by means of estimation of suitable mixing matrix. Each column of the mixing matrix represents a spatial map that projected the weights of the corresponding temporal component at each EEG electrode. These spatial maps and temporal waveforms of decomposed independent components are categorized into task-related and task-unrelated groups respectively. This separation would effectively speed the classification of EEG patterns. The task-related EEG signals were taken and classified using adaptive pattern classifier which consists of combing the Kohonen Self-Organizing Map (SOM) with Learning Vector Quantization (LVQ). The algorithm was trained and tested using offline EEG signals measured according to ten-twenty International system obtained from a computerized EEG system in Ibn-Rushd Hospital, and the obtained results of the recognition rate were 75.