A windbreak wall structure is provided to adhere and fix a support and a windbreak plate stably by placing a brace on one side of a windbreak plate and inserting a wedge between a brace and a rear flange. The windbreak wall structure for minimizing the influence of a wind on a bridge railing comprises supports(310) such as H-posts installed on a concrete foundation by anchor bolts and placed at regular intervals along the bridge railing, and plural windbreak plates(320) placed between a front flange(312) and a rear flange(313) of the support vertically to be adhered closely to the front flange of the support and equipped with a brace(325) spaced out from the rear flange of the support and a wedge(326) placed in a gap between the brace and the rear flange to make the windbreak plate adhered/fixed closely to the support.