A variable steering gear mechanism (9) is constructed of an external gear (15) connected to an input shaft (11), an internal gear (16) fixed to housing (10) and meshing with the external gear (15), an intermediate member (19) receiving a rotary force transmitted from the external gear (15), change means (18a, 31, 33a) capable of changing a rotation ratio of the output shaft (33) to a rotation of a guide member (18), and an Oldham coupling (17) connecting the intermediate member (19) to the guide member (18). When a speed reduction ratio thereof is set to, e.g., 6:1, it follows that the input member (18) of the change means makes a ¼ rotation (rotates through 90 degrees) during one-sided 1.5 rotations (540 degrees) of the input shaft (11), whereby a characteristic of the change means can be effectively utilized. A gear mechanism such as a hypocycloid mechanism has a characteristic capable of, though compact in configuration, obtaining a speed reduction ratio as large as 6:1, and also such a characteristic that the external gear (15), in addition to the self-rotation, revolves around the axis line of the internal gear (16), i.e., rotates while being eccentric. By contrast, according to the present invention, the use of the Oldham coupling (17) enables only the self-rotation to be extracted and transmitted by absorbing the eccentricity of the external gear (15). Additionally, a meshing length between the external gear (15) and the internal gear (16) becomes large, whereby smoother power transmission can be attained.