The electroencephalogram (EEG) isconsidered to be one of the most scientifically exploitedsignals recorded from a human's organism. The difficultyencountered in the processing of the EEG signal stemsfrom its highly non-stationary and complex nature. Itappears that time-frequency (t-f) analysis of theelectroencephalogram is one of the most popularapproaches to the extraction of knowledge about braindynamics. This paper presents the Matching Pursuit (MP)method used for obtaining t-f features from braincomputerinterface (BCl) data, in this case the EEGsignals recorded from a subject performing imaginationof left and right hand movement. The emphasis in thepaper is put on an effective realization of MP with Gabordictionary due to its intensive computational load.Genetic Algorithms (GAs) have been utilized to optimizethe performance of the t-f method under consideration,which has resulted in the implementation of a GeneticMatching Pursuit Algorithm (GMPA). The BCI data areclassified using linear discriminant analysis (LDA) basedon the set of features extracted with the help of theGMPA. The applicability of the technique to a BCI systemis verified on the basis of the classification accuracy (CA)rate.