We propose a two-dimensional (2D) polymer-walled liquid-crystal (LC) phase-grating device, which can be used to control the haze with a very low power. 2D polymer walls can be formed in an LC cell through ultraviolet light irradiation while applying an in-plane electric field through phase separation induced by the spatial elastic energy difference. The transparent and translucent states can be realized by applying vertical and in-plane electric fields to the 2D polymer-walled LC cell, respectively. The cell can be operated with a very low power as the transparent [translucent] state is maintained even after the applied vertical [in-plane] electric field is removed. It consumes power only during state switching. The fabricated device exhibits outstanding performances, such as a very low operating voltage (< 10 V), low haze (< 2%) in the transparent state, high haze (> 90%) in the translucent state, and short switching time (< 2 ms), compared to those of other bistable LC devices, which can be used to control the haze.