The metamaterials with negative Poisson’s ratio are called auxetic materials, which as a branch of metamaterials has drawn a lot of attention in many areas. Existing auxetic knitting textiles combine flexibility and auxeticity, however the loose structure has been a main disadvantage for its application. In this study, we fabricated Miura origami structure fabrics by weaving technology in order to acquire more stable auxetic textiles. The results show that using the combination of fabric structure type and elastic yarns, an origami structure can be realized in a jacquard loom. In the Miura origami structure, the crease pattern can be separated into three parts, unfolding areas, convex areas, and concave areas. One warp system and two weft systems are compounded together, in which a weft backed weave is used to get elastic floats in the convex and concave areas, and to make the fabrics bend to the concave side. The physical map showed that the fabrics had a clear Miura origami structure and the unfolding areas were flat and even. On the basis of the designed geometric pattern, weft backed weaves can be used to construct different folded areas, spandex wrapped PET (Polyester) and inelastic PET are selected as two weft systems for weaving. Meanwhile, the Miura origami fabrics exhibit distinct in-plane negative Poisson’s ratio and out-of-plane positive Poisson’s ratio. Apart from the Miura origami structure, other origami and paper-cut structures can be realized using this method, and these special auxetic textiles have potential in protective cloths, ornamented textiles, wearable devices, and flexible sensors.