A new three-dimensional structural optimization is presented based on the level set method to obtain favorable designs for wire-fed metal additive manufacturing with uniform wall thickness. By exploiting the signed distance nature of a level set function, a structure under design is always defined as a thin domain with uniform thickness without employing any constrains or penalty functionals. The boundary surfaces of a thin-walled domain are defined as the surfaces with level set values of ±t/2(t: wall thickness). Design velocity can be represented in terms of curvatures of the zero-level-set surface, extended to level set grids in the narrow band. Therefore, the calculation of accurate curvatures on the zero-level set is crucial for correct design sensitivities. In this investigation, mean and Gaussian curvatures at a point on the triangle mesh of the discretized zero-level set are calculated by spatial averages over the Voronoi cell of the point, by which the sensitivity of a material volume can be calculated with optimal accuracy. To address the high computational cost by a dense regular mesh for representing thin walls, degrees of freedom in void regions is mostly removed. Design examples of beams and a T-joint structure with uniform thickness are presented to verify the effectiveness of the proposed method.