Decoding the user intention from non-invasive EEG signals is a challenging problem. In this paper, we study the feasibility of predicting the goal for controlling the robot arm in self-paced reaching movements, i.e., spontaneous movements that do not require an external cue. Our proposed system continuously estimates the goal throughout a trial starting before the movement onset by online classification and generates optimal trajectories for driving the robot arm to the estimated goal. Experiments using EEG signals of one healthy subject (right arm) yield smooth reaching movements of the simulated 7 degrees of freedom KUKA robot arm in planar center-out reaching task with approximately 80 % accuracy of reaching the actual goal.