Stereoscopic augmented reality (AR) displays with a fixed focus plane suffer from visual discomfort due to vergenceaccommodation conflict (VAC). In this study, we propose a biocular dual-focal plane AR system. Two separate liquid crystal displays (LCDs) are placed at slightly different distances to a Fresnel relay lens such that virtual images of LCDs appear at 25 cm and 50 cm to the user. Both LCDs are totally viewed by both eyes, such that the rendered images are not parallax images for each eye. While the system is limited to two depths, it provides correct focus cues and natural blur effect in two distinct depths. This allows the user to distinguish virtual information, even when the virtual objects overlap and partially occlude in the axial direction. Displays are driven by a single computation unit and the objects in the virtual scene are distributed over the LCDs according to their depths. Field-of-view is 60 x 36 degrees and the eye-box is larger than 100 mm, which is comfortable enough for two-eye viewing.