To construct and evaluate a novel wheelchair system that can be freely controlled via electroencephalogram signals in order to allow people paralyzed from the neck down to interact with society more freely. A brain-machine interface (BMI) wheelchair control system was constructed by effective signal processing methods, and subjects were trained by a feedback method to decrease the training time and improve accuracy. The implemented system was evaluated through experiments on controlling bars and avoiding obstacles using three subjects. Furthermore, the effectiveness of the feedback training method was evaluated by comparison with an imaginary movement experiment without any visual feedback for two additional subjects. In the bar-controlling experiment, two subjects achieved a 95.00% success rate, and the third had a 91.66% success rate. In the obstacle avoidance experiment, all three achieved success rate over 90% success rate, and required almost the same amount of time to reach as that when driving with a joystick. In the experiment on imaginary movement without visual feedback, the two additional subjects adapted to the experiment far slower than they did with visual feedback. In this study, the feedback training method allowed subjects to easily and rapidly gain accurate control over the implemented wheelchair system. These results show the importance of the feedback training method using neuroplasticity in BMI systems.