Performing some special tasks using electrooculography (EOG) in daily activities is being developed in various areas. In this paper, simple rotation matrixes were introduced to help the operator move a 2-DoF planar robot manipulator. The EOG sensor, NF 5201, has two output channels (Ch1 and Ch2), as well as one ground channel and one reference channel. The robot movement was the indicator that this system could follow gaze motion based on EOG. Operators gazed into five training target points each in the horizontal and vertical line as the preliminary experiments, which were based on directions, distances and the areas of gaze motions. This was done to get the relationships between EOG and gaze motion distance for four directions, which were up, down, right and left. The maximum angle for the horizontal was 46°, while it was 38° for the vertical. Rotation matrixes for the horizontal and vertical signals were combined, so as to diagonally track objects. To verify, the errors between actual and desired target positions were calculated using the Euclidian distance. This test section had 20 random target points. The result indicated that this system could track an object with average angle errors of 3.31° in the x-axis and 3.58° in the y-axis.