The invention discloses a weft yarn curve woven fabric, a weaving method thereof and a special elastic free reed thereof. Weft yarns of the woven fabric are in a curved shape. The weaving method comprises pacing of warp, opening, wefting insertion, beating-up and take-up, and is characterized in that during the beating-up, the elastic free reed of which the dent is bent according to beating-up force is adopted; the filling rate of the woven fabric which is in the weft direction on a weaving machine in the same line is different from the change of fabric weaves or the thickness change of weft yarns, so that the beating-up force varies; when the elastic free reed is subjected to the beating-up, the dent is bent according to the beating-up force, namely the filling rate is large, so that thebending of the dent is large; and the filling rate is small, so that the bending of the dent is small to realize weft yarn curves. In the weaving method, the conventional horizontal and vertical weaving form is changed, the weft yarns of the woven fabric are in the curved shape, and if colored threads are used, beautiful curved patterns can be generated, so the grade of woven fabric varieties canbe improved.