Biosignals will play an important role in building communication between machines and humans. One of the types of biosignals that is widely used in neuroscience are electrooculography (EOG) signals. An EOG has a linear relationship with eye movement displacement. Experiments were performed to construct a gaze motion tracking method indicated by robot manipulator movements. Three operators looked at 24 target points displayed on a monitor that was 40 cm in front of them. Two channels (Ch1 and Ch2) produced EOG signals for every single eye movement. These signals were converted to pixel units by using the linear relationship between EOG signals and gaze motion distances. The conversion outcomes were actual pixel locations. An affine transform method is proposed to determine the shift of actual pixels to target pixels. This method consisted of sequences of five geometry processes, which are translation-1, rotation, translation-2, shear and dilatation. The accuracy was approximately 0.86° ± 0.67° in the horizontal direction and 0.54° ± 0.34° in the vertical. This system successfully tracked the gaze motions not only in direction, but also in distance. Using this system, three operators could operate a robot manipulator to point at some targets. This result shows that the method is reliable in building communication between humans and machines using EOGs.