Electroencephalography is a non-invasive measure of the brain electrical activity generated by millions of neurons. Feature extraction in electroencephalography analysis is a core issue that may lead to accurate brain mental state classification. This paper presents a new feature selection method that improves left/right hand movement identification of a motor imagery brain-computer interface, based on genetic algorithms and artificial neural networks used as classifiers. Raw electroencephalography signals are first preprocessed using appropriate filtering. Feature extraction is carried out afterwards, based on spectral and temporal signal components, and thus a feature vector is constructed. As various features might be inaccurate and mislead the classifier, thus degrading the overall system performance, the proposed approach identifies a subset of features from a large feature space, such that the classifier error rate is reduced. Experimental results show that the proposed method is able to reduce the number of features to as low as 0.5% (i.e., the number of ignored features can reach 99.5%) while improving the accuracy, sensitivity, specificity, and precision of the classifier.