In order to measure the relative position of the Stewart platform for the subreflector of a dual-reflector antenna, the monocular vision based position measurement system is studied and designed. A cooperative target fixed on a moving platform by light source is proposed. Combined with the filter and other control means, the monocular camera is applied to collect the image of non-coplanar feature points, and the quasi ideal image with high contrast is obtained. The image coordinates of the feature points are extracted, and the relative position measurement method of the Stewart platform is obtained by using Efficient Perspective-n-Point (EPnP) algorithm. Finally, the accuracy is verified by experiments. The results show that the translation accuracy is 0.1 mm and the rotation accuracy is 0.05^\circ, which meets the experimental requirements, and provides a feasible idea for the position detection of the Stewart platform.