When a length is measured using a plane array device, reaching submicron-level accuracy is difficult because of the limitation imposed by the pixel size of the plane array device and subdivision technique. Therefore, we propose a method for measuring two-dimensional submicron displacements based on the multibeam interference principle of the Fabry-Perot (F-P) etalon. A two-dimensional micro-displacement in the focal plane is obtained by calculating the variation of the center coordinate of a concentric interference ring. The virtual plane array pixel subdivision technique and peak-position coordinate local subdivision technology are used to process the massive information of the plane array. In this way, the influence of undetermined systematic error is reduced, which allows an accurate calculation of the center coordinate of the concentric interference ring. The experiment uses an F-P etalon with an interval of approximately 2 mm and a optical lens with focal length about 50 mm. The center of the imaging concentric interference ring is calculated at different positions in the focal plane. The results show that the measurement range can reach 3 mm. The experiment uses a laser phase-modulating homodyne interferometer for the comparison measurements. The results show that in the range of 34 μm, the linear fitting standard deviation of the measured results is 0.0154w″ and the extended uncertainty is 0.036w″ when the coverage factor is 2.45, where w″ is the relative pixel interval. These results confirm the accuracy of the measurement method.