Head mounted displays (HMD) showed huge market potential in recent years. In these techniques, vergenceaccommodation conflict (VAC) is a fundamental problem which makes viewers feel discomfort and fatigue. To overcome this limitation, researchers proposed many solutions including Maxwellian view displays, vari-focal plane displays, multifocal plane displays, integral imaging-based displays, and computational multilayer displays. These techniques can enable correct or nearly correct focus cues, however, they failed to achieve both high image fresh rate and high lateral resolution with a compact architecture. In this paper, we propose a compact birefringent-based virtual reality (BVR) HMD with correct focus cues by spatially projecting the input images onto four depth planes. In the BVR, two stacked liquid crystal displays (LCDs) provide two axially separated input images in an additive fashion. We set a liquid crystal panel behind the LCDs to modulate the polarization of the emitting light from the LCDs pixel-wise. After that, a birefringent lens and an eyepiece project the modulated light onto four depth planes at 0D, 1D, 2D, and 3D. To minimize the astigmatism of the system, we employ a birefringent doublet with orthogonal optic axes and use an eyepiece to suppress the overall aberration. Comparing to the existing techniques, the proposed BVR mitigates the VAC problem with a compact architecture. Moreover, because there is no temporal multiplexing and lateral resolution sacrifice, the BVR can easily achieve high image refresh rate and high lateral resolution. Herein, we present the optical design of the BVR and characterize its performance in Zemax.