Brain- Computer Interface (BCI) is used to control a system through which people with motor disabilities could achieve a better quality of life by improving their interaction ability with the surrounding environment. Using BCI, patients suffering from severe motor disabilities can also control variety of applications by generating control commands using their own EEG signals. There are many assistive devices are available to reduce the personal, social, and economic burdens of their disabilities and improve their independence but many of these individuals do not have the normal neuromuscular pathway for using their hands to control an assistive device. Hence, EEG could be used to control artificial arm which can help those people to interact with their physical environment and carry out their activity of daily living. In this paper, a genetic algorithm is proposed for trajectory planning of an EEG controlled robotic arm. EEG data for motor imagery were captured from five healthy subjects and left-right hand movement was classified using Support Vector Machine classifier (SVM) with the feature used as Power feature co-efficient and wavelet co-efficient. EEG processing and GA algorithm was developed using Matlab.