In this paper, we present our novel design for switchable AR/VR near-eye displays which can help solve the vergence-accommodation-conflict issue. The principal idea is to time-multiplex virtual imagery and real-world imagery and use a tunable lens to adjust focus for the virtual display and the see-through scene separately. With this novel design, prescription eyeglasses for near- and far-sighted users become unnecessary. This is achieved by integrating the wearer's corrective optical prescription into the tunable lens for both virtual display and see-through environment. We built a prototype based on the design, comprised of micro-display, optical systems, a tunable lens, and active shutters. The experimental results confirm that the proposed near-eye display design can switch between AR and VR and can provide correct accommodation for both.