This paper introduces a robot eye module, of which two degree-of-freedom motions, i.e. panning and tilting, are driven by a pair of wires. The main feature of the module is that each wire can generate push-pull motion without buckling. It is thanks to a Teflon tube which guides the path of the moving wire. End points of the tube and wire have pivot elements so that a smooth push-pull motion is produced even when the end point of wire is moved by eye rotation. This mechanism helps the eye module to be very compact. In this paper, the structure of the robot eye module is introduced in detail, and the required motor angles for a certain direction of eye line are investigated analytically and experimentally.