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A genetic algorithm (GA)-based neural network classification in the application of brain computer interface (BCI) for controlling a wheelchair is presented in this paper. This study uses an electroencephalography (EEG) as a non-invasive BCI approach to discriminate three non-motor imagery mental tasks for disabled individuals who may have difficulty in using BCI based motor imagery tasks. The three tasks classification is mapped into three wheelchair movements: left, right and forward and the relevant combination mental tasks used in this study are mental arithmetic, letter composing, Rubik's cube rolling, visual counting, ringtone imagery and spatial navigation. The results show the proposed system provides good classification performance after selecting the most effective of three discriminative tasks across combination of the different non-motor imagery mental tasks for the five subjects tested. The average classification accuracy is between 76% and 85 %, with information transfer rates varies from 0.5 to 0.8 bits per trial.